Colloidal Science of Ultrasound Contrast Agents

A Thesis

Submitted to the Faculty

of

Drexel University

by

Stephen Michael Dicker

in partial fulfillment of the

requirements for the degree

of

Doctor of Philosophy

May 2012

© Copyright 2012

Stephen M. Dicker. All Rights Reserved

ii

DEDICATIONS

I dedicate this work to my wife, Lindsay. This wouldn’t have happened without you.

iii

ACKNOWLEDGMENTS

My first and foremost acknowledgement should and must go to my advisor, Dr. Steven

Wrenn. By whatever gift of luck, I had the opportunity to work with an advisor who at all times, through high and low points, was always genuinely interested in my betterment and success. I owe any measure of success I have so far achieved to him. Additionally, my work was significantly impacted by the tireless work of Michał Mleczko, and the devoted Masters students whose work aided mine at every step, Alexandra Bartolomeo and James Dierkes. I am also grateful for the support and guidance of my thesis committee, Dr. Peter Lewin, Dr. Nily Dan, Dr. Guiseppe Palmese, and Dr. Anthony

Lowman, who have all made measurable impacts on my development during my time at

Drexel.

My time at Drexel has been thoroughly enjoyable thanks to the support of my Drexel coworkers and friends. My past and present group mates, Angela Brown, Mike Walters,

Nicole Wallace, Alyi Bartolomeo, Jim Dierkes, Sam MacLean and Ellie Small have made even the most tedious work bearable. In other groups I thank Julianne Holloway,

Erik Brewer, Michael Marks, Lauren Conova, Jason Coleman, Siamak Nejati, Mona

Bavarian, Ali Emileh, Pat Kirby, Fela Odeyemi, and Amy Peterson for their constant support and friendship. I was also lucky enough to receive the opportunity to travel to

Bochum, Germany for a semester, and receive the tutelage of Dr. Georg Schmitz. My time in Germany was both a pleasure and success in no small part to my group members iv

there, in particular Michał Mleczko, Karin Hensel, Markus Hesse, Monica Siepmann,

Martin Beckmann, and Martin Schiffner. To all of my friends and colleagues, domestic

and abroad: your kindness and camaraderie will never be forgotten.

I am also grateful to my collaborators: Dr. Andrzej Nowicki of the IPPT PAN in Warsaw,

Poland, Dr. Ari Brooks of the Drexel University College of Medicine in Philadelphia,

PA, and Dr. Kathleen Boesze-Battaglia of the University of Pennsylvania Dental School in Philadelphia, PA.

The work was supported by the National Science Foundation, grant CBET-1064802, the

George Hill endowed fellowship, and the Deutscher Akademischer Austauschdienst,

program number D/08/45370.

Finally, my path has led me thus far only with the support of my parents, David and

Mary-Alice Dicker, my brother, Kevin Dicker, and my wife, Lindsay Dicker. My

journey had been shaped by you four who deserve all acclaim for anything I have

attained.

v

TABLE OF CONTENTS

LIST OF TABLES ...... ix

LIST OF FIGURES ...... x

ABSTRACT ...... xv

CHAPTER 1: A Brief History of Ultrasound Contrast Agents ...... 1

1.1 The Invention of Ultrasound ...... 1

1.2 Clinical Ultrasound ...... 2

1.3 Ultrasound Contrast Agents ...... 9

1.3.1 Ultrasound Contrast Agent History ...... 10

1.3.2 Microbubble Chemistry ...... 13

1.4 Microbubble Cavitation ...... 19

1.4.1 Stable Cavitation ...... 20

1.4.2 Inertial Cavitation ...... 22

1.5 Microbubble Dynamic Radius ...... 26

1.5.1 The Rayleigh-Plesset-Neppiras-Noltingk-Poritsky equation ...... 27

1.6 Dissertation Summary ...... 36

CHAPTER 2: Microbubble Size Distributions ...... 38

2.1 Introduction ...... 38

2.2 Microbubble Synthesis and Image Segmentation ...... 39

2.2.1 Materials ...... 39

2.2.2 Microbubble Preparation ...... 40 vi

2.2.3 Microbubble Size Determination ...... 41

2.3 Size Distribution ...... 46

2.4 Incorporation into Subsequent Chapters and Conclusion ...... 50

CHAPTER 3: Microbubble Inertial Cavitation Threshold Pressure...... 52

3.1 Introduction ...... 52

3.2 Inertial Cavitation Detection ...... 55

3.2.1 Materials ...... 55

3.2.1 Microbubble Preparation ...... 55

3.2.3 Cavitation Detection Technique ...... 56

3.3 Microbubble Acoustic Response ...... 65

3.4 Transducer Calibration...... 67

3.5 Cavitation Threshold Pressure as a Function of Shell Composition ...... 70

3.6 Simulating Inertial Cavitation Thresholds ...... 77

3.6.1 The Herring Equation ...... 78

3.6.2 Morgan's Modification of the Herring Equation ...... 79

3.7 Conclusion ...... 90

CHAPTER 4: Colloidal Model for Microbubble Oscillations ...... 96

4.1 Significant Microbubble Dynamics Models ...... 96

4.1.1 Naked Microbubble Models ...... 96

4.1.2 Thinly Shelled Microbubble Models ...... 99

4.1.2.1 de Jong Model ...... 100

4.1.2.2 Morgan Model ...... 103

4.1.2.3 Marmottant Model ...... 106 vii

4.2 Colloidal Approach to Microbubble Dynamics ...... 109

4.3 Simulating Cavitation with the Colloidal Model ...... 115

4.3.1 Simulation Method...... 116

4.3.2 Cavitation Profile Sensitivity ...... 119

4.4 Predictive Model for Microbubble Cavitation ...... 124

4.5 Conclusion ...... 131

CHAPTER 5: Resonance Frequency of Microbubbles ...... 132

5.1 Introduction to Resonance Frequency ...... 132

5.2 Detection of Microbubble Resonance Frequency ...... 133

5.2.1 Materials ...... 133

5.2.2 Microbubble Preparation ...... 134

5.2.3 Resonance Frequency Measurement...... 135

5.3 Reference Spectrum and Concentration Calibration...... 138

5.4 Resonance Frequency as a Function of Shell Composition ...... 142

5.5 Simulating Resonance Frequency ...... 145

5.6 Dependence of Cavitation Threshold on Resonance Frequency ...... 152

5.7 Effect of Shell Mass ...... 154

5.8 Conclusion ...... 157

CHAPTER 6: Co-encapsulation Ultrasound Contrast Agent ...... 165

6.1 Co-encapsulation Introduction ...... 165

6.2 Design of Co-encapsulated Contrast Agent ...... 167

6.2.1 Materials ...... 167

6.2.2 Microbubble Preparation ...... 168 viii

6.2.3 Microcapsule Synthesis ...... 169

6.3 Clinical Imaging of Contrast Agents ...... 175

6.4 Acoustic Response of Contrast Agents ...... 180

6.5 Contrast to Tissue Ratio ...... 188

6.6 Cavitation Behavior of Co-Encapsulated Microbubbles ...... 197

6.6.1 Cavitation Measurements...... 197

6.6.2 Modeling Co-encapsulated Oscillation Behavior ...... 200

6.7 Cavitation Induced Cell Death ...... 202

6.8 Co-encapsulation Microcapsule Leakage Studies ...... 209

6.8.1 Calcein: Self-quenching Fluorophore ...... 210

6.8.2 Low Frequency Dye Leakage ...... 214

6.8.3 Clinical Frequency Dye Leakage ...... 218

6.9 Conclusion ...... 220

CHAPTER 7: Summary and Implications ...... 223

7.1 Project Summary ...... 223

7.2 Implications...... 225

7.3 Future Outlook ...... 227

LIST OF REFERENCES ...... 230

APPENDIX A: List of Abbreviations...... 241

APPENDIX B: List of Symbols ...... 243

VITA ...... 246 ix

LIST OF TABLES

1.1 Ultrasound Contrast Agent Overview ...... 14

2.1 Matrix of studied shell compositions ...... 40

3.1 Modified Herring equation model parameters ...... 81

5.1 Hoff equation model parameters ...... 147

x

LIST OF FIGURES

1.1 Sound spectrum ...... 3

1.2 Amplitude mode scan ...... 3

1.3 Brightness mode fetal ultrasound...... 7

1.4 Optison boxed warning ...... 12

1.5 Microbubble schematic cross-section ...... 15

1.6 Distearoyl phosphatidylcholine molecule ...... 17

1.7 Polyethylene glycol repeating unit ...... 18

1.8 PEG membrane configurations ...... 18

1.9 Stable Cavitation ...... 21

1.10 Screw propeller cavitation damage ...... 23

1.11 Inertial cavitation streak image ...... 24

1.12 Microbubble oscillation in a liquid ...... 28

1.13 Incident pressure function ...... 33

1.14 Microbubble dynamic response as predicted by Rayleigh's equation ...... 33

1.15 Microbubble response predicted by the RPNNP equation ...... 35

2.1 Typical microbubble micrograph ...... 43

2.2 Inverted binary microbubble micrograph ...... 44

2.3 Polygon outlined microbubbles ...... 45

2.4 Size distribution histogram ...... 47

2.5 Microbubble mean diameter as a function of shell composition ...... 48 xi

3.1 Field simulation of a transducer ...... 57

3.2 Cavitation detection experimental set-up ...... 58

3.3 Cavitation detection schematic ...... 59

3.4 Phase inversion technique ...... 61

3.5 Conditions for an undestroyed microbubble ...... 62

3.6 Conditions for a destroyed microbubble ...... 63

3.7 Acoustic response of various microbubble concentrations ...... 66

3.8 2.25 MHz transducer calibration...... 69

3.9 Representative bubble destruction curve ...... 71

3.10 Influence of PEG molecular weight and composition on cavitation thresholds ...... 73

3.11 PT50 cavitation pressure dependence on PEG molecular weight and composition ...... 74

3.12 Cavitation threshold variance as a function of microbubble size polydispersity for the 90 mole% DSPC / 10 mole% DSPE-PEG2000 system ...... 76

3.13 Herring equation optimal cavitation size ...... 83

3.14 Theoretical Herring model comparison with experimental data ...... 84

3.15 Range of relevant χ and µsh values ...... 85

3.16 Theoretically determined inertial cavitation thresholds ...... 86

3.17 Error surface for a given shell composition ...... 88

3.18 Plane of best fit input parameters ...... 89

4.1 RPNNP and modified Herring model comparisons ...... 98

4.2 RPNNP and de Jong model comparison ...... 102

4.3 Morgan model predictions ...... 104 xii

4.4 Morgan model predictions of the Mach number ...... 105

4.5 Marmottant and Morgan model predictions ...... 109

4.6 Colloidal model oscillation predictions ...... 113

4.7 Colloidal model Mach number predictions...... 115

4.8 Prediction for the incidence of cavitation ...... 117

4.9 Comparison of measured size distribution with "destruction distribution" ...... 118

4.10 Predicted sensitivity to cavitation threshold ...... 120

4.11 Predicted sensitivity to area expansion modulus ...... 121

4.12 Predicted sensitivity to dilatational viscosity ...... 122

4.13 Predicted sensitivity to surface tension ...... 123

4.14 Mushroom regime cavitation profiles ...... 125

4.15 Mushroom regime fitted cavitation profile ...... 126

4.16 Predicted KA for various shell compositions ...... 128

4.17 Brush regime predicted cavitation profile ...... 130

5.1 Resonance frequency detection setup ...... 136

5.2 Acoustic views of the chirp ...... 137

5.3 Reference acoustic spectrum...... 139

5.4 Effect of microbubble concentration on resonance frequency ...... 141

5.5 Microbubble frequency dependent attenuation ...... 143

5.6 Measured microbubble resonance frequency as a function of shell composition ...... 144

5.7 Theoretical resonance frequencies ...... 149

5.8 Finding best fits of resonance frequency ...... 150

5.9 Modeled solutions for a set of contrast agents ...... 151 xiii

5.10 Experimental cavitation threshold and resonance frequency comparison ...... 153

5.11 Expected resonance frequency based on shell mass ...... 156

6.1 Contrast agent micrographs ...... 169

6.2 W/O/W double emulsion ...... 170

6.3 Microcapsule SEM image ...... 172

6.4 Encapsulation of fluorescent microbubbles within double emulsion particles ....173

6.5 Brightness mode ultrasound image of microcapsules with co-encapsulated microbubbles ...... 175

6.6 Normalized acoustic brightness of contrast agents ...... 177

6.7 Raw acoustic brightness of contrast agents ...... 178

6.8 Tissue harmonic images (THI) ...... 179

6.9 Acoustic response graphs ...... 182

6.10 Shelf life of synthesized contrast agents ...... 184

6.11 Concentration effects on the acoustic response of contrast agents ...... 186

6.12 Contrast to tissue ratio phantom ...... 189

6.13 Phase inversion mode ultrasound images of co-encapsulated contrast agent ....190

6.14 Contrast to tissue ratio of co-encapsulated contrast agent and SonoVue ...... 191

6.15 CTR of Definity and the co-encapsulated contrast agent ...... 194

6.16 CTR under continuous ultrasound ...... 196

6.17 Inertial cavitation threshold of co-encapsulated and un-encapsulated microbubbles ...... 199

6.18 Oscillations predicted for co-encapsulated microbubbles ...... 202

6.19 PI fluorescence cell death assay ...... 204

6.20 Cell death as a function of microbubble/capsule concentration ...... 206 xiv

6.21 Cell death and cavitation profiles ...... 208

6.22 Calcein concentration calibration ...... 211

6.23 Interactions between calcein and latex ...... 213

6.24 Fluorescent dye leakage with low frequency ultrasound ...... 216

6.25 Active ultrasound leakage from co-encapsulated microcapsules ...... 217

6.26 Mechanism of vesicle budding from a bilayer ...... 219

6.27 Pulse jet vesicle synthesis ...... 220

7.1 Ruptured co-encapsulated microcapsule...... 229

xv

ABSTRACT Colloidal Science of Ultrasound Contrast Agents Stephen Michael Dicker Advisor: Steven P. Wrenn, Ph.D.

In this work, the behavior and properties of microbubble ultrasound contrast agents are measured and theoretically analyzed. Among these measurements are the microbubble size distribution, inertial cavitation threshold, and resonance frequency. The size distributions of populations of microbubbles are examined with a variety of different shell compositions. The size distributions are very similar for all the shell compositions measured; they contained a monomodal peak with a nearly Gaussian distribution. The mean size of the microbubbles did not change significantly for the compositional changes made in this study. This same set of microbubble shell compositions is then analyzed for their resonance frequency. This is accomplished by measuring the attenuation of a broadband chirp signal sent through a field of microbubbles and the frequency where the attenuation is the greatest the resonance frequency. It is found that as PEG mole fraction and molecular weight increase, the resonance frequency decreases. These shell compositions are then analyzed for their inertial cavitation threshold pressure and the results show that as PEG mole fraction increases, the inertial cavitation threshold increases. With increasing PEG molecular weight, however, the cavitation threshold decreases.

xvi

With these experimental cavitation results, a predictive model is desired to explain the

data theoretically. Based on the colloidal science principles, a new model for the oscillation of thinly shelled microbubbles is explained. For simple microbubble compositions, a predictive model can be applied for calculating material parameters of the microbubble shell. This equation is shown to hold for the experimental cavitation data collected during the course of this work.

Using the information gathered in the previous chapters, a novel contrast agent was

designed. The contrast agent is comprised of lipid microbubbles within the aqueous core

of polymer shell microcapsules. This combination has the benefit of added patient safety

(through the aversion of cell death) while providing similar contrast to commercially

available contrast agents. The contrast agent accomplishes this by shielding the

microbubbles from the incident sound pressure and preventing their expansion beyond

the threshold radius. The design of the contrast agent is also inherently a drug delivery

vehicle which caters to both hydrophilic and hydrophobic drugs.

2

CHAPTER 1: A Brief History of Ultrasound Contrast Agents

1.1 The Invention of Ultrasound

As you’ve probably heard, the British luxury cruise ship R.M.S. Titanic struck a large

iceberg on the evening of April 14th, 1912, and sunk just 3 hours later. This was

considered a great tragedy, and in order to avoid such future incident, Paul Langevin decided that ships of this nature needed a way to detect these types of scurrilous icebergs

[1]. Langevin had previously been a student of the famous Pierre Curie (and illicit lover of Pierre’s more famous wife), and was well versed in one of Curie’s many discoveries, piezoelectricity. His solution to the iceberg question was the invention of the hydrophone

(along with Constantin Chilowski), a device which could produce high frequency sound above the range at which human ears can hear (above 20 kHz) and listen for reflections of

the sound off of underwater geography, like icebergs [2]. Four years later, the

hydrophone became quite popular and useful for detecting German U-boats tormenting

conventional surface bound Allied ships [2]. This method of pulse echo location is the same which is used by bats and dolphins to guide their movements in the dark, and is the precursor to the modern ultrasound transducer.

It wasn’t until the 1950’s when an esteemed Professor of Midwifery at Glasgow

University, Ian Donald, used ultrasonic pulse echo location for medical techniques; more specifically for fetal imaging, it’s most prevalent use today [3]. However, this one 3

dimensional amplitude line (or “A-mode”) was not sufficient for any imaging purposes,

as it only draws a line of the reflection intensity of the ultrasound signal. As so, in 1962,

Joseph Holmes, William Wright, and Ralph Meyerdirk invented the commonly used and

stereotypical 2-D ultrasound system known as Brightness mode (or B-mode) ultrasound

imaging system [4]. B-mode images are those most commonly seen in film and

Facebook pictures of gestating children. As recently as the early 2000s, 3-D ultrasound

has become a reality (can also be considered as 4-D since the image can be watched in

real time) and is commonplace in larger clinics and hospitals [1]. Today, ultrasound is

an important tool in the clinical setting for both diagnostic imaging and a range of

therapeutics (such as lithotripsy, cancer treatment, and cosmetic surgery [5, 6]).

1.2 Clinical Ultrasound

Ultrasound is simply defined as a mechanical vibration (otherwise known as sound) at frequencies above 20 kHz, the upper limit of human hearing [7]. This frequency of sound can be generated by the vibrations created by a piezoelectric material, such as lead- zirconate-titonate (PZT) or polyvinylidene fluoride (PVDF) [1]. Piezoelectric materials are ideal for this technique as they can transform an electric signal into mechanical vibrations, therefore creating sound at a user defined pressure amplitude (akin to volume) and frequency (pitch). Additionally, piezoelectric materials have backwards functionality; they can transform mechanical vibrations into an electric signal. These 4

received signals can be used to build an ultrasound image. For these reasons, the

business end of an ultrasound system, the transducer, is made of a piezoelectric material.

Figure 1.1: Sound spectrum. The audible sound spectrum is between 20 Hz and 20 kHz, with infrasound

being below the audible range, and ultrasound above.

The original application of ultrasound, finding icebergs underwater, is quite simple. The

primitive ultrasound transducer, or hydrophone, emits a quick burst of sound then listens

for reflections of that sound from any objects in the sound’s path, and how long it takes from when the sound is emitted until it is detected. These one dimensional Amplitude or

A-mode scans simply display the magnitude (or amplitude) of the reflected sound being

picked up by the hydrophone against the time between transmission and detection. A-

mode “images” are reminiscent of submarine films, in which a tracer line scrawls across

screen, beeping to indicate the presence of an enemy vessel.

5

Figure 1.2: Amplitude mode scan. A typical A-mode line is shown, simply tracing the amplitude of the

received signal (vertical axis) against the travel time of the pulse. The spikes indicate strong

reflections which are above a set threshold for detection. Between the spikes is the level of

noise [8].

In the scan from Figure 1.2, the tracer plots the pressure amplitude of the sound wave on

the vertical axis against the total time from when the transducer emitted the sound to

when it receives it (travel time). Travel time is directly related to the distance an object is

from the transducer (z):

2 = 푧 푡푡푟푎푣푒푙 푐 (Equation 1.1)

where c is the speed of sound in water (1500 m/s). The distance is doubled because the

sound needs to travel to and from the object it is reflecting off of. Also of note from

Figure 1.2 is the amplitude of the received signal. The amplitude spikes indicate echoes

coming from a certain distance from the transducer, which likely represent some real

object detected underwater; whether it represents a fish, U-boat, or iceberg is

indeterminate. The steady, low values in A-mode are background noise, seen in Figure

1.2 between the spikes and after the second spike.

When sound is transmitted into a media, it propagates in the normal direction until the sound signal is lost to either reflection or attenuation [9-11]. Reflection is the rebound of the transmitted sound off an object in the sound’s path which can be picked up by the 6

transducer and translated into an image. The amplitude of sound reflected from an object

is determined by the comparison of the acoustic properties of the materials on either side

of the object-water interface. The acoustic properties can be summed up by the acoustic impedance (Z), measured in Rayleighs (or Rayls) named after the famous sound pioneer

Lord Rayleigh:

Z = c

i i i ρ (Equation 1.2)

where ρ is the density of the material. The amount of sound reflected off a given

interface can then be determined with the reflective index (RI):

| | = 2 + 1 퐼 푍 − 푍 푅 2 1 푍 푍 (Equation 1.3)

where the subscripts 1 and 2 denote the materials on either side of the interface [1]. From

Equation 1.3, it is obvious that materials with similar acoustic impedances will have a reflective index close to zero, meaning close no reflections. Materials which have very dissimilar acoustic impedances (like water and submarine steel) will have a reflective index close to unity, indicating nearly total reflectance. These reflections from interfaces are what build the trace in Figure 1.2, with the amount of reflected sound being related to the amplitude. To solve the problem of sound reflection in diagnostic imaging, a gel matching layer is applied between the transducer and the patient’s skin. This gel layer 7

has a similar acoustic impedance to human tissue in order to minimize reflections (tissue

acoustic impedance = 1540 m/s) [1]. Without this matching layer, the sound would be transmitted into a thin air layer between the transducer and skin, then reflect substantially off the air-skin interface (Zair = 400 Rayl, Ztissue = 1.5 MRayl; RI (air-tissue) = 0.999). If

this were the case, only 0.1 % of the transmitted signal would pass through the air-skin

interface and be available for imaging.

These reflections are again employed when adding a dimension to the ultrasound image,

and moving into Brightness, or B-mode. Through the use of array transducers (multiple

element), two dimensional images can be generated by compiling the information

gathered from the multiple transducer elements. In this mode, each transducer element

(typically at least 64 elements) builds a line propagating longitudinally through the

adjoining media. The quintessential B-mode image of a fetus is shown below in Figure

1.3.

8

Figure 1.3: Brightness mode fetal ultrasound. B-mode image of an 18 week old fetus (the author’s

nephew, David Dempsey) taken with a curved array transducer is displayed. Different

materials translate into a grayscale based on the magnitude of their reflection coefficient

(white = bone, tissue = grey, amniotic fluid, blood = black).

The image of the fetus is easily recognizable because of the acoustic impedance

difference between the materials shown in the image. Sound propagates from the

transducer (top of the image) downwards towards the bottom of the image. The

trapezoidal shape of the image matches the shape of the transducer array (in this case a

curved array). As the echoes are received by the transducer, an image can be built based

on the travel time from when the sound pulse was emitted to when the echo was received,

and the magnitude of the echo (as in A-mode). Modern ultrasound systems have sufficient computer processing speed to update these images in real time (25 – 30 frames per second) [1].

The colors on the grayscale represent the magnitude of the reflections from the various material interfaces. Black represents the materials which have the least reflection (blood, or amniotic fluid), the grays are materials which have some degree of reflection (tissue, organs), and white represents the greatest reflection (bone, air). The skull is clearly recognizable in white, along with the ribs of the fetus. The black streaks traveling through the fetus’ head are acoustic shadows, areas in which all the sound has already been reflected (in this case most likely by the skull) and no signal is received, thus no image is compiled. In clinical settings, a thin gel matching layer is applied to the patient’s skin to avoid small air pockets between the skin and the ultrasound transducer 9 from reflecting the signal. The majority of human tissue has a very similar acoustic impedance to water (1.5 MRayl for water, 1.6 MRayl for tissue), as does the matching layer gel (1.5 MRayl).

The other mechanism by which a sound signal is lost is through attenuation of the signal by the media it is travelling through. Total attenuation is basically the losses in the signal due to sound adsorption and irregularities in the material the sound is propagating through. Attenuation (measured in dB per MHz per cm) is dependent on both the travel distance of the sound and the sound frequency. For both dependences, the total amount of sound attenuated increases for higher frequencies and travel distances. Given the frequency, all sound will be attenuated by a certain distance from the transducer and will be worthless for pulse echo location. The attenuation coefficient (measuring the degree of attenuation per MHz per cm) changes depending on the material the sound is traveling through. For example, the attenuation coefficient is very low in water, with a value of

0.002 dB/(MHz cm), increases to 0.14 dB/(MHz cm) for blood, and to 3.54 dB/(MHz cm) for bone [1]. For this reason, sound propagates the farthest through water without being completely attenuated of the three materials listed above. The heterogeneous nature of human tissue leads to unpredictable non-linearity in the signal, along with additional incidences of signal scattering and reflection [12].

Besides losses and reflections in tissue, ultrasound imaging also suffers from inherent flaw which limits the usefulness of the technique. It is well known that the sound frequency (f) is equal to the speed of sound (c) divided by the wavelength (λ): 10

= 푐 푓 휆 (Equation 1.4)

The problem is the well known trade-off between ultrasound image resolution and penetration depth. The image resolution is related to the wavelength of the sound wave, such that the smaller the wavelength, the better the resolution (smaller objects can be resolved). Since wavelength is inversely proportional to the frequency of the sound, the higher the selected imaging frequency, the higher the image resolution will be. However,

attenuation of the signal through tissue also rises (at 0.5 dB/ (MHz cm)) with the increase

of frequency, limiting the image adequacy at higher penetration depths. Therefore, there

is some optimal ultrasound frequency to give the best image depending on the penetration

depth required. This optimum frequency depends on the several clinical variables, such the size of the object being imaged and patient weight (lower frequencies required for increased depth through adipose). Most clinical ultrasound machines have at least three

transducers for achieving optimal resolution depending on the penetration depth and

resolutions required for the specific application and circumstance.

1.3 Ultrasound Contrast Agents

Current ultrasound imaging techniques have the advantage of being a relatively safe, inexpensive, and non-invasive diagnostic tool when compared to other imaging 11 modalities like computed axial tomography (CAT), magnetic resonance imaging (MRI), and X-ray [1]. However, ultrasound imaging suffers in image resolution and depth of view compared to these techniques and is therefore inadequate for many diagnostic scenarios. For example, it is difficult to resolve small blood vessels, such as 10 µm diameter capillaries [7, 13], because of their size coupled with the acoustic similarities between blood and tissue. To aid in overcoming this issue, ultrasound contrast agents are employed to enhance the picture quality of ultrasound images in situations such as the one mentioned above.

1.3.1 Ultrasound Contrast Agent History

The first use of ultrasound contrast agents occurred in 1968 by cardiologists Raymond

Gramiak and Pravin Shah [14]. Gramiak and Shah noted that when injecting agitated saline solution into a heart chamber during echocardiology, a so-called cloud of echoes could be resolved from the chamber, which is perturbed and dissipates with subsequent heart beats. This cloud of echoes can be attributed to the reflection of the ultrasound signal from gas pockets in the injected saline solution created during agitation. The reflections are simply caused by the mismatch in the acoustic impedance between air and blood, and thus the ultrasound contrast agent was born. However, this technique suffered because of the short lifespan of the contrast agent, as the agitated gas within the saline quickly dissolves in the larger volume of blood. On the other extreme, if too much air is added into the bloodstream an embolism can develop, and more than 20 ml of air can be fatal [15, 16]. Therefore, small, stable gas bubbles are ideal for increased bubble lifetime and avoiding emboli. 12

As ultrasound technology developed, so did the need for effective and safe contrast

agents. In 1982, the first commercially available contrast agent, Echovist, was released

by Berlex Canada. To stabilize the micron sized gas bubbles, the interface of the

microbubbles is coated with galactose granules. In this way the air bubbles will resist dissolution in the bloodstream and retain a size smaller than that of the smallest capillary

(10 µm) [17]. The first FDA approved contrast agent used in the US was Albunex (since discontinued) in 1994, which was only approved for echocardiology (Albumin shell with

encapsulated air). Since their commercial inception, ultrasound contrast agents have

grown significantly in their medical utility. Besides being integral in echocardiology,

they are of particular interest in cancer diagnosis, specifically in their ability to

distinguish between benign, fluid-filled cysts, and malignant, vascular tumors [6, 18].

Outside the realm of diagnostic imaging, microbubbles were also being evaluated as drug

delivery vehicles (their ability to trigger drug release preferentially when under

ultrasound will be discussed later in this chapter). However, this microbubble research

renaissance was to be ended by an FDA black box warning on ultrasound contrast agents.

In October 2007, the FDA issued a black box warning (like those found on cigarettes) for

all contrast agents listing a litany of potential contraindications of contrast agent use.

Whether this warning was deserved was to be a matter of much debate in Washington

and abroad. It was reported that several patients who had been administered an

ultrasound contrast agents reported complications on the day after imaging occurred, with

at least one of these instances being a fatality [19]. Naturally, regulatory agencies like 13

the FDA reacted quickly by issuing the black box. In Europe, Bracco’s SonoVue was

withdrawn from the market because of European regulator’s concerns over possible

respiratory distress caused by the dissolved heavy gas [19]. However, more recent

studies have shown that these measures may have been an overreaction. First, it is

unclear whether use of ultrasound contrast agents was the cause of the complications and

death. These effects could have been from the ultrasound itself, some other non-related

factor, or most likely the pre-existing heart condition they required an echocardiograph

for. Secondly, and more convincingly, it has been reported that the safety records from

echocardiography indicate only a 1:500,000 fatality risk, which is lower than that for the

other imaging modalities mentioned earlier [20, 21].

Figure 1.4: Optison boxed warning. This FDA regulated black box warning appears on GE

Healthcare’s Optison as of January 2012.

Regardless of deservedness, the 2007 black box warning severely crippled the ultrasound

contrast agent industry. Many outdated and startup manufacturers were forced to fold,

and even a current industry leader – GE Healthcare’s Optison – was temporarily removed

from the market. Through the lobbying effort of healthcare professionals, in particular

Philadelphia’s own Dr. Barry Goldberg, some of the warnings were relaxed only a year

later in 2008, albeit not totally removed [22]. Although only present for a year, the effects of the black box warning were felt even by the largest manufacturers, and to date only three have weathered the warning: GE Healthcare’s Optison, Lantheus’ Definity, 14

and Bracco’s SonoVue (although SonoVue is in the European market). A fourth

manufacturer, Acusphere, currently has an ultrasound contrast agent in the pipeline,

which is expected to be commercially available as soon as it gains FDA approval. Most

recently, in October 2011, Lantheus won another major victory for the industry by further

removing contraindications from the packaging of Definity [22]. While the industry was

crippled for almost 4 years from the FDA warning, it is finally beginning to regain favor

from doctors and researchers alike in the advancement of medical imaging and drug

delivery. Today, ultrasound contrast agents are still only FDA approved for

echocardiology, however abroad (especially in Europe and South America) contrast

agents are approved for a wide range of diagnostic applications [22]. The commercial

use of microbubbles as drug delivery vehicles has yet to be accepted, although it can be anticipated in the near future with the state of research towards that end [6].

1.3.2 Microbubble Chemistry

The importance of stability has been at the forefront of ultrasound contrast agent technology development. Since 1982, contrast agents have gone through developmental

“generations” in their pursuit of increased stability [12]. Michiel Postema and Georg

Schmitz compiled a comprehensive list of the current state of the microbubble contrast industry in 2006 (adapted and updated in Table 1.1) [12]. As evident from Table 1.1, the ultrasound contrast agent industry has suffered significantly since 2006 due to the black

box warning.

15

Table 1.1: Ultrasound contrast agent market overview. Adapted from Postema and Schmitz [12].

Mean Product Diameter Current Name Manufacturer Shell Material Gas (µm) Availability Molecular Albunex Albumin Air 4.3 No Biosystems Levovist, Lipid/galactose, Schering AG Air 2-3 No Sonovist cyanoacrylate Lantheus

Definity Medical Lipid/surfactant C3F8 1.1 - 3.3 Yes Imaging

Echogen Sonus Pharm. Surfactant C5F12 2 – 5 No Alliance Imagent Lipid/surfactant C F 6 No Pharm. 6 14

Optison GE Healthcare Albumin C3F8 2.0 – 4.5 Yes Quantison Upperton Ltd. Albumin Air 3.2 No

SonoVue Bracco Lipid SF6 2.5 Yes AI-700 Polylactic co- Acusphere C F 2 Pipeline (Imagify) glycolic acid 4 10 Point Cardiosphere Polylactic acid Air 3 No Biomedical

Sonozoid GE Healthcare Lipid/surfactant C4F10 2.4 – 3.6 Japan only

The first generation, as typified by Echovist, is defined by a coated microbubble with encapsulated air. The coatings of the first generation of microbubble contrast agents were typically sugars or proteins [1, 12]. The main drawback of this first generation of contrast agents was the relatively high solubility of air in the bloodstream (0.0292 vol/vol in water) [23]. To further improve stability, the second generation of contrast agents was comprised of microbubbles which encapsulate a lower solubility gas, such as perfluorocarbons or sulfur hexafluoride (SF6). Many of these inert gasses have water solubility of an order of magnitude lower than air (0.007 vol/vol in SF6) [23]. The 16 microbubble coatings also became more stabile with the introduction of phospholipid and polymer shells, and often a blend of both. This type of microbubble contrast agent is the most prevalent in the industry today, and is therefore the focus of the experiments, simulations, and discussions in this dissertation.

Figure 1.5: Microbubble schematic cross-section. The cartoon shows a phospholipid monolayer

microbubble encapsulating a gas core with some percent of the lipids functionalized with

polyethylene glycol (PEG) polymer.

As shown in the cartoon in Figure 1.5, the microbubbles synthesized in this study (which are a close analog of SonoVue or Definity) contain only three species. First, the microbubble shell encapsulates a gas core, which for this work (and SonoVue) is SF6.

The monolayer phospholipid shell surrounding the core needs to be in the gel phase in 17 order to successfully encapsulate the gas. The lipid chemistry that best satisfied the condition of a gel phase at room (or body) temperature are those whose fatty acid chains are completely saturated – that is, the fatty acid chains contain only single bonds. Double bonds in the fatty acid chains of phospholipids decrease the melting point and the packing efficiency of the membrane, both of which are unfavorable for gas encapsulation [24].

The benefit of using phospholipids as the coating for microbubbles is their ability to self- assemble because of their molecular structure. The hydrophilic head group will always seek to align itself close to the aqueous, while the hydrophobic fatty acid tail groups will seek to shield themselves from the water. In the case of a microbubble, the tail groups can minimize their free energy by coating the gas interface. The lipid used most predominately in phospholipid shelled microbubbles is Distearoyl phosphatidylcholine

(DSPC), a molecule with two fatty acid chains of 18 single bonded carbons, with a choline head group (as seen in Figure 1.6).

18

Figure 1.6: Distearoyl phosphatidylcholine molecule. 2-D and 3-D molecular models of DSPC as

shown. Like all phospholipids, it contains a hydrophilic head group (choline) a

phosphate/glycerol linker, and a hydrophobic tail group (two stearic acids).

To further increase the stability of the microbubble, some fraction of the monolayer lipids can be functionalized with a hydrophilic polymer. Most commonly, the polymer selected for these purposes is some form of Polyethylene glycol (PEG). PEG is preferable because of its relatively high hydrophilicity amongst polymers, and because of its biocompatibility. PEG increases the stability of microbubbles simply by the steric repulsion of the PEG chains protruding from two different microbubbles, which keeps the bubbles from coalescing. The same effect aids microbubble longevity in the 19 bloodstream, and the PEG repels macrophages employed in the reticuloendothelial system from breaking down the microbubbles [7, 25, 26].

Figure 1.7: Polyethylene glycol repeating unit. PEG has a molecular formula of C2nH4n+2On+1, where n

is the number of repeat units.

The percentage of lipid functionalized PEG in the membrane and (to a lesser extend) the molecular weight of the PEG influence the surface properties of the polymer. At relatively low PEG functionalization, the polymer has space sufficient to exhibit a more random structure (with one end grafted to the lipid), better known as the mushroom regime. As PEG functionalization increases, the polymer strands begin to feel the presence of the others in the membrane and begin to straighten and stand upright, normal to the membrane [27]. This densely packed formation is known as the brush regime.

Both polymer configurations are displayed below in Figure 1.8.

20

Figure 1.8: PEG membrane configurations. At low functionalization percentages, defined by

Backmann [27] as when the distance between two polymer grafting points is approximately

greater than twice the polymer radius, the PEG polymer is free to spread out to its natural

radius of gyration in the mushroom regime. When the distance between two polymers is less

than twice the polymer radius, the two strands begin to repulse each other and therefore

straighten into the brush regime.

As shown in Figure 1.8, the PEG configuration transitions from mushroom to brush regime when the distance between two PEG strands drops below twice the polymer radius. At this point the strands are repulsing one another, since the PEG strands have a stochastic position, with their probable positions shown in Figure 1.8 as green hemispheres [27].

This combination of encapsulated low solubility heavy gas, a gel phase lipid monolayer, and a percentage of the membrane lipid functionalized with PEG leads to a stable ultrasound contrast agent.

1.4 Microbubble Cavitation

When microbubbles are exposed to an ultrasound field, they will begin to oscillate radially to the “tune” of the sound. That is, the microbubbles are feeling the alternating positive and negative pressures imposed by the sound wave. Microbubbles are sufficiently small that the entire microbubble will always experience the same acoustic 21 pressure; it is a point charge to the ultrasound wave (i.e. for 3 MHz ultrasound traveling through water, the wavelength will be 500 µm, much larger than a 1 µm bubble) [28].

Therefore, during the positive portion of the wave, the microbubble will experience increased external pressure, and begin to contract. On the negative portion of the pressure cycle, the microbubble will be experience a negative external pressure and will expand. These oscillations are made possible by the compressible gas core, where other microstructures may feel the vibrations from the sound wave; few will be affected as dramatically as bubbles. This oscillatory phenomenon is generally referred to as cavitation.

1.4.1 Stable Cavitation

Cavitation can be broken down into two categories, based on the outcome of the oscillations. Stable cavitation can be defined if linear microbubble oscillations are sustained indefinitely under an unchanging ultrasound field. Linear oscillations are those in which the positive and negative responses of the microbubble are equal in magnitude

(to match the ultrasound sine wave signal). In this case, as depicted in Figure 1.9

(adapted from Chomas [29]), the microbubble contracts under positive pressure and expands under negative pressure indefinitely.

22

Figure 1.9: Stable cavitation. The microbubble size responds to the incident acoustic wave in two ways,

as imaged by Chomas [29] and redrawn by Szabo [1]. The speed of the oscillations is

determined by the frequency of the sound wave, and the magnitude of the oscillations is

dependent on the pressure amplitude of the sound wave.

Sustained stable cavitation occurs at low pressure amplitudes, specifically those below

the inertial cavitation threshold pressure. Altering the frequency of ultrasound also has an effect on the dynamic radius of the microbubble. As frequency increases, the effects of the microbubble shell cause the response of the microbubble to lag behind the frequency of the incident sound [30, 31]. Because of this lag, the microbubble never has sufficient time during a single cycle to reach the size dictated by the maximum pressure amplitude of the sound wave. That is to say, while the microbubble is decreasing in radius in response to the positive pressure, it begins to experience the negative pressure portion of the cycle before it has fully responded to the positive pressure portion, and therefore begins to grow (again lagging behind the incident sound wave). This lag can be attributed partially to the dampening effect from the mass of the shell [32]. At lower 23

frequencies, the microbubble will have sufficient time to fully respond to the oscillations

from the incident sound wave and grow to their full potential.

As a result of the oscillating microbubble, the surrounding fluid is also pulled towards

and pushed away from the bubble in a process known as microstreaming.

Microstreaming is the first example of the microbubble’s ability to influence its

environment as a result of oscillation. The effects of microstreaming have been shown

by Wu to transiently open cell membranes to which a microbubble has been tethered, in a

process known as sonoporation [33]. Wu also reports that the shear stress induced on a

cell bilayer from the microstreaming of a tethered microbubble to be as high 10 kPa [34].

In the scope of microbubble cavitation bio-effects, microstreaming is a minor contribution as compared to those from inertial cavitation.

1.4.2 Inertial Cavitation

When microbubble oscillations become sufficiently large in magnitude, they can undergo a violent collapse known as inertial cavitation. In the event of inertial cavitation, a microbubble grows too large during its negative pressure expansive phase that it implodes on itself in the subsequent positive pressure rarefactional phase. This implosion is accompanied by a large local increase in temperature and pressure, suggested by Szabo to be up to 5000 K and 100 MPa respectively [1]. Along with these local effects, a shockwave is generated by the imploding bubble, which can impart a large positive pressure on nearby structures. This phenomenon was first observed in naval research, as the speed at which boat propellers spin causes gas voids to form and subsequently 24 collapse behind the propeller blades. The negative pressure behind the blades was sufficient to nucleate these gas voids, which then inertially cavitated as they returned to the hydrostatic pressure, causing damage to the propeller (as seen in Figure 1.10).

Figure 1.10: Screw propeller cavitation damage. Evidence of the power of inertial cavitation is

obvious at the bottom of the image.

The criterion for the onset of inertial cavitation is a matter of some debate in the ultrasound field. Initially it was thought by most groups and published in The Acoustic

Bubble [35] (otherwise known as The Acoustic Bible, in some circles) that this inertial cavitation criteria was the bubble reaching approximately twice its initial radial, R = 2R0.

This idea is especially popular amongst groups who are able to measure the size of an oscillating bubble, using high speed photography techniques which are capable of recording 10 million images per second [29, 36]. They note that when a bubble reaches twice its resting size during the expansion phase, it will generally collapse on the subsequent rarefactional phase, as demonstrated in Figure 1.11 (again from Chomas

[29]). Other groups suggest that criteria for inertial cavitation should be related to the 25 bubble wall velocity, or the kinetic energy [37]. More specifically, a suitable cavitation threshold might be defined as when the bubble wall speed exceeds the speed of sound in the surrounding media (the definition of the onset of a shockwave).

Figure 1.11: Inertial cavitation streak image. This streak image, generated by Chomas [29], shows the

radius of the microbubble as a function of time during sonication. In the first image, the

microbubble is at its resting radius, R0, and ultrasound has yet to be applied. As ultrasound

is applied, at approximately 0.6 µs, the positive pressure phase causes the bubble to

contract. At 0.9 µs, the bubble has fully expanded in response to the negative pressure peak

of the incident ultrasound, which upon inspection is greater than twice the resting radius.

On the subsequent positive pressure phase, the microbubble undergoes an implosion,

displayed at starting at 1 µs.

The streak image by Chomas clearly shows a microbubble, initially at rest, undergoes a growth phase followed by a fragmentation, collapse, and destruction. As this process is quite chaotic, the outcome of the destruction is somewhat nebulous. While it is obvious from Figure 1.11 that the bubble is destroyed, it is difficult to ascertain whether its 26

disappearance can be attributed to a high energy collapse (like inertial cavitation), or

rather a fragmentation or dissolution.

The onset of high energy inertial cavitation is the suspected cause of the many of the

negative bio-effects associated with contrast enhanced ultrasound imaging [20].

Microbubbles which inertially cavitate while tethered to cells are likely to cause cell

death. Those which are inertially cavitate in the bloodstream also have a chance to cause

hemolysis [20]. As these results are unwanted during an ultrasound scan, ultrasound

vendors coined a variable to aid clinicians in avoiding unwanted adverse effects. The

mechanical index (MI) is defined as:

= 푃푁푃 푀퐼 �푓 (Equation 1.5)

where PNP is the peak negative pressure of the incident sound wave (in MPa) and f is

center frequency of the incident sound (in MHz). In practice, it is only FDA approved to

operate a clinical unit under an MI of 1.9 [38]. Quite evidently, the mechanical index is an empirical parameter with odd units which is used as a rough guideline for avoiding inertial cavitation and unwanted adverse effects. In general, the MI illustrates two factors which influence the likelihood of the onset of inertial cavitation; an increase in the acoustic pressure leads to larger oscillations of the microbubble (thus approach the cavitation threshold), and a decrease in the frequency allows longer times for microbubbles to nucleate and grow in response to the negative pressure they are under 27

(also approaching sizes near the threshold). This is quite a simplistic approach to avoiding adverse bio-effects, and therefore a better understanding of the parameters which affect the onset of cavitation is highly desirable, and is discussed at length in

Chapter 3.

However, in some cases the onset of inertial cavitation is favorable. These cases are generally confined to the realm of drug delivery. Cavitation can aid drug delivery in two ways. First, as discussed previously, the cavitating microbubble can cause reversible pores to open in the membrane of a cell, therefore better allowing drug present in the cell’s environment to enter through these pores; a process known as sonoporation [39,

40]. Secondly, the microbubbles themselves can act as the drug carriers. In these cases, a hydrophobic drug can be added to the surfactant shell of the microbubble and as the microbubble ruptures, the small pieces of the shell can be more easily taken up by the cells [15, 41, 42]. This strategy would be especially effective against cancer cells, as they are known to have a so-called “leaky” vasculature in which to trap microbubble fragments containing the drug [25, 41, 43]. Both the potentially positive and negative effects related to inertial cavitation make it and its onset topics of interest for pharmacologists and clinicians alike.

1.5 Microbubble Dynamic Radius

28

These cavitation effects were being felt as early as the turn of the 20th century. With the

growing popularity of the steam engine as the main use of propulsion for warships and

other naval vessel and the advent of the gas turbine, ship propellers were being driven

faster than ever. The screw propeller (from Figure 1.10) in particular was almost

exclusively used with these forms or propulsion. However, as discussed earlier, these

types of propellers were easily damaged just by normal use as the result of inertial cavitation. This problem is precisely what attracted a prominent thinker of the time to analyze the phenomenon in detail: John William Strutt, otherwise known as Lord

Rayleigh.

In 1917, Lord Rayleigh was 75 years old and had accomplished more than many scientists combined in a lifetime (and in fact Rayleigh would be dead just 2 years later).

His greatest achievements to date included the explanation of why the sky is blue

(Rayleigh scattering) and discovering the element argon (for which he won the Nobel

Prize). He would add to his long list of credentials by expounding - along with the contributions of four others - the most fundamental equation of bubble motion, still in use today (albeit with many modifications).

1.5.1 The Rayleigh-Plesset-Neppiras-Noltingk-Poritsky Equation

The Rayleigh-Plesset-Neppiras-Noltingk-Poritsky equation, or RPNNP as it is affectionately known [44], is the basis for the understanding of bubble oscillations. Lord

Rayleigh originated the equation to describe the collapse of an empty cavity in an incompressible fluid (to mimic those collapsing behind propeller blades) [45]. Along 29

with Lord Rayleigh, the next 3 contributors to the equation, Milton Spinoza Plesset in

1949 [46], Ernest Neppiras and B.E. Noltingk in 1950 and 1951 [47, 48], were all interested in modeling the microbubble size phenomenon. Neppiras and Noltingk were the first to study the oscillations of naked (with no shell) microbubbles under the influence of ultrasound [48]. However each of the first four contributors derived this non-linear bubble motion equation, starting from a simple energy balance. A brief

schematic of the process is show below in Figure 1.12.

Figure 1.12: Microbubble oscillation in a liquid. The initial microbubble radius R0, is changing with

the R (or R(t)) in response to an incident ultrasound wave with pressure P(t). PI is the

internal pressure of the bubble, PL is the pressure directly outside the bubble, P0 is the

hydrostatic pressure, and P∞ is the pressure far away from the bubble.

The initial energy balance of the system is simple. The work of a microbubble expanding

(or contracting) can be equated to the kinetic energy of the fluid being moved by the

microbubble.

30

1 = 2 2 � 푃푑푉 푚푣 (Equation 1.6)

where P is pressure, V is bubble volume, m is the mass of liquid being moved, and v is

the velocity at which it is moving. In Equation 1.6 the left hand side represents the PV

work of the bubble, and the right hand side is the kinetic energy of the fluid being

displaced (assuming expansion). The volume on the left and the mass on the right can

then be rewritten as a function of the bubble radius, R, and the velocity on the right as a

function of the radial position, r, starting at the outside of the bubble, R.

1 ( )4 = 4 2 2 2 푑푟 2 � 푃퐿 − 푃∞ 휋푅 푑푅 휌 � � � 휋푟 푑푟 푑푡 (Equation 1.7)

where PL is the pressure directly outside the bubble, P∞ is the pressure far away from the

bubble, R is the dynamic bubble radius, ρ is the density of the liquid, and r is the radial

position outside the bubble, and is the bubble wall velocity, and will be written as . 푑푟 푑푡 To simplify the equation, r can be rewritten as a function of R from a simple mass푟̇

balance. If the liquid is incompressible, then the conservation of mass result can be written as in Equation 1.8.

= 4 2 2 푅 푅̇ 푟 ̇ 4 푟 31

(Equation 1.8)

Now substituting Equation 1.8 into Equation 1.7 and solving the integral on the right hand side only between R and infinity,

( )4 = 2 2 4 2 � 푃퐿 − 푃∞ 휋푅 푑푅 휋휌푅 푅̇ (Equation 1.9)

To remove the integral on the left, the derivative of both sides of the equation can be

taken with respect to R. Taking the derivative of the right hand side gives Equation 1.10:

( )4 = 2 3 + 2 2 2 2 3 푑푅̇ 푃퐿 − 푃∞ 휋푅 휋휌 � 푅 푅̇ 푅 � �� 푑푅 (Equation 1.10)

The dR term in the denominator of the final term on the right can be equated dt (by the

푅̇ definition of . Now taking the derivative of , 2 푑푅̇ 푅̇ 푑푡

( )4 = 2 3 + 2 2 2 2 3 퐿 ∞ ̇ 푃 − 푃 휋푅 휋휌� 푅 푅 푅 푅̈ � (Equation 1.11)

32 where is the second derivative of bubble radius with respect to time (bubble wall ̈ acceleration).푅 Finally, P∞ can be equated to P0 plus the ultrasound pressure function, P(t), and the equation can be quickly rearranged to its familiar form:

3 1 + = ( ( )) 2 2 푅푅̈ 푅̇ 푃퐿 − 푃0 − 푃 푡 휌 (Equation 1.12)

However, PL is a quantity which is practically impossible to measure, and therefore it is easier to recast it in terms of the pressure inside the bubble, PI, and the Laplace pressure:

2 = + 휎 푃퐼 푃퐿 푅 (Equation 1.13)

where σ is the surface tension. Next, both immeasurable pressures should be removed from the equation. If the process is adiabatic, then PVγ is constant (where γ is the polytropic index). Therefore, the initial state of the equation can be equated to the state of the equation at any time t.

= 훾 훾 푖푛푖푡푖푎푙 푃푉 푃 푉 0 (Equation 1.14)

2 4 2 4 + = + 3 훾 3 훾 휎 3 휎 3 �푃퐿 � � 휋푅 � �푃0 � � 휋푅0� 푅 푅0 33

(Equation 1.15)

2 2 = + 3훾 0 퐿 0 휎 푅 휎 푃 �푃 0� � � − 푅 푅 푅 (Equation 1.16)

By combining Equation 1.16 and Equation 1.12, the final form of the equation is arrived

at (as derived by Neppiras and Noltingk [48]):

3 1 2 2 + = + ( ) 2 3훾 2 휎 푅0 휎 푅푅̈ 푅̇ ��푃0 � � � − − 푃0 − 푃 푡 � 휌 푅0 푅 푅 (Equation 1.17)

Elegant as this solution is, it is somewhat incorrect. First, the solution is quite unstable

and only holds for small oscillations in R (low pressures, below 100 kPa). Another

inherent flaw becomes obvious when P(t) becomes zero after some time, t (as if the ultrasound is shut off), the bubble oscillations persist undampened beyond when P(t) becomes zero. Figure 1.13 show the shape of the pressure function, P(t), used throughout this work (although at varying amplitudes). Its characteristic is the 4 cycle sine wave, followed by 2 µs of rest (to allow the radius to return to rest). Figure 1.14 shows the dynamic response of the microbubble radius (normalized by the resting radius), as predicted by Equation 1.17 (when ρ is 998 kg/m3, P0 is 10.13 kPa, σ is 0.051 N/m, γ is

1.07, and R0 is 1 µm). 34

Figure 1.13: Incident pressure function. The incident pressure function here and throughout this work

is characterized by a 4 cycle sine wave pulse, followed by 2 µs of rest. Here, the pressure

amplitude is 100 kPa, although this is varied significantly throughout this work.

35

Figure 1.14: Microbubble dynamic response as predicted by Rayleigh’s equation. The

microbubble’s predicted change in normalized radius over time is shown here to be non-

linear response to the 100 kPa pressure function shown in Figure 1.13 (as expected).

However, the radial oscillations persist even after the pressure function is zero, indicating a

flaw in the equation.

This undamped oscillation issue was fixed quickly however by the fifth and final contributor to the equation in 1952, made by Poritsky [49]. Poritzky derived an equation for the same situation, although instead of approaching the derivation with an energy balance, Poritsky used a common fluid dynamics relationship, the Navier-Stokes equation. From this derivation, he arrived at the same result, with an added term. This term amounts to the viscous losses in pressure as attributed to the notion that the liquid has some viscosity (which they do). Therefore, with its final addition, the complete

RPNNP equation is as follows in Equation 1.18:

3 1 2 2 4 + = + ( ) 2 3훾 2 휎 푅0 휎 휇푅̇ 푅푅̈ 푅̇ ��푃0 � � � − − − 푃0 − 푃 푡 � 휌 푅0 푅 푅 푅 (Equation 1.18)

where µ is the viscosity of the liquid. A simulation of the complete RPNNP equation, as seen in figure below, shows that if P(t) becomes zero, the bubble radius with dampen back to its initial value. Figure 1.15 show the response predicted by the RPNNP with the same P(t) and input parameters (with µ = 0.001 Pa s) as used to generate Figure 1.14.

36

Figure 1.15: Microbubble response predicted by the RPNNP equation. With the same P(t) and input

parameters as used to generate Figure 1.14, the RPNNP equation proves superior as the

viscous losses term dampens the oscillations of the bubble after the pressure is reduced to 0

(at about 2 µs).

The RPNNP equation does operate under a set of assumptions however, which are as follows [50, 51]:

1. The bubble is always spherical.

2. Uniform conditions exist within the bubble.

3. The acoustic wavelength is large compared to the bubble size (such that

the whole bubble always experiences the same pressure.

4. No body forces are accounted for (such as gravity or electromagnetism).

5. Bulk viscous effects are ignored. 37

6. The surrounding liquid is incompressible, but the bubble gas is not.

7. The density of the surrounding fluid is far greater than that of the gas.

8. The gas content of the bubble is always constant.

9. The vapor pressure of the gas is always constant.

10. The bubble oscillations are adiabatic.

11. The bubble has no coating (nothing between the gas and liquid).

Although all these assumptions are not entirely sound, it has been the work of many groups since the 1950s to account for many of these shortcomings of the RPNNP equation. The one focus in particular, especially in the past two decades, has been in accounting for an oscillating microbubble which does have a coating or shell, as is the case with ultrasound contrast agents. Several of such equations will be presented in the following chapters, along with proposed model for microbubble dynamic radius from a colloidal and membrane science viewpoint. All of these equations however, find their roots in the RPNNP equation.

1.6 Dissertation Summary

This dissertation will focus mainly on five topics: the effect of varying the shell composition on the size of microbubbles, cavitation phenomenon, and resonance frequency, along with the design of a microbubble oscillation model and the design and implications of a novel ultrasound contrast agent. As the size distribution of a population 38 of microbubbles significantly influences its cavitation and resonance behavior, it will be discussed briefly in Chapter 2. Chapter 3 focuses on the development of a technique to measure inertial cavitation and the influence of shell composition on the cavitation threshold of microbubbles. This behavior will also be modeled with a RPNNP-like equation in such a way to better understand cavitation phenomena. Chapter 4 will briefly discuss various proposed models for microbubble dynamic radius, along with the development of a new model to describe the oscillations as a function of colloidal parameters. Chapter 5 introduces the effect of changes in shell composition on the resonance frequency of microbubbles, along with a technique for measuring resonance frequency experimentally and a theoretical explanation.

Using the information in the preceding chapters, Chapter 6 describes the design of a novel contrast agent with the focus of contrast longevity, patient safety, and potential dual functionality as a drug delivery vehicle. Techniques developed in previous chapters will be used to analyze the new contrast agent, such as cavitation measurements and acoustic response data. Additionally, an equation to describe microbubble oscillations for the new contrast agent is developed. The final chapter, 7, reviews the significant findings of this work and attempts to project the future direction of research relating to these studies.

39

CHAPTER 2: Microbubble Size Distributions

2.1 Introduction

As evident from equations like the RPNNP, the size of a bubble is important to

understand as it determines the point at which the bubble will cavitate [52, 53]. The real- time size of a microbubble under an ultrasound field is non-linear and chaotic (very sensitive to initial conditions), and it is most often preferred to consider the initial, or resting radius of the microbubble instead. The resting radius (R0 in the equations herein)

greatly influences the response of the microbubble to the ultrasound field, and can

determine the likelihood of cavitation (if the threshold is related to R/R0). As a simplifying assumption in some RPNNP-like equations, the microbubble size is taken to be a constant [54, 55]. In the case of analyzing the theoretical behavior of a single microbubble, this can be of some merit. However, when analyzing a large population of microbubbles like those present in ultrasound contrast agents, the microbubble size is often highly varied.

In real scenarios, the synthesis or manufacturing procedure will set the resting size of a microbubble. Small scale techniques, such as microfluidics, have the advantage of great sensitivity and can consistently synthesize microbubbles with very uniform sizes [56].

Larger scale techniques, such as those employed by Bracco and Lantheus in the production of their respective contrast agents, do not have the luxury of a perfectly 40

uniform size in their formulations. In the case of Definity, for example, a previously

prepared mixture of dissolved lipid and heavy gas are sealed and vigorously mixed at the

time of injection. This mixing process creates stable microbubbles between 1.1 – 3.3 µm

in diameter, as reported by Lantheus [12]. The shape of the distribution of these sizes is roughly Gaussian. Successful techniques such as these can produce a large quantity of microbubbles in a short time at high concentrations. Again, the trade off is the apparent distribution of sizes. In microbubble populations like Definity, SonoVue, and those synthesized in this work, it is important to bear the size distribution in mind the when comparing experimental results with theoretical models. This chapter presents the method in which the microbubbles used in this study are synthesized along with a novel image segmentation program for measuring the size distribution of microbubble contrast agents, and the resulting size distributions of the microbubble compositions discussed herein.

2.2 Microbubble Synthesis and Image Segmentation

2.2.1 Materials

The lipid 1,2-Distearoyl-sn-Glycero-3-Phosphocholine (DSPC) and Polyethylene Glycol

(PEG) functionalized lipid 1,2-Disteroyl-sn-Glycero-3-Phosphoethanolamine-N-

[Methoxy(Polyethyleneglycol)-2000], ammonium salt (DSPE PEG 2000) were purchased

from Avanti Polar Lipids (Alabaster, AL). The 1000, 3000 and 5000 g/mole molecular weight DSPE PEG functionalized lipids were also supplied by the above. Sulfur 41

Hexafluoride (SF6) gas was purchased from Airgas (Allentown, PA). All other reagents

used were of analytical grade.

2.2.2 Microbubble Preparation

Preparing phospholipid shelled microbubbles is a simple self-assembly process. A lipid

film containing various mole% of the gel phase lipid DSPC (85 – 99 mole%) and a PEG

functionalized lipid (1 – 15 mole%) is deposited onto a 20 ml scintillation vial from stock

solutions dissolved in chloroform by N2 spin drying followed by 2 hours in vacuum. A matrix of the shell compositions analyzed in this chapter (and in the following chapters) is gathered in Table 2.1, along with the mass of lipid and PEG functionalized lipid mixed to synthesize them.

Table 2.1: Matrix of studied shell compositions. The masses (in mg) of materials used to

synthesize the microbubbles of the various shell compositions are displayed in the matrix.

%mole DSPE PEG DSPE PEG DSPE PEG DSPE PEG PEG 5000 DSPC 3000 DSPC 2000 DSPC 1000 DPSC 1 1.11 52.09 0.74 53.47 0.56 54.16 0.36 54.90 2.5 2.53 45.97 1.75 49.70 1.34 51.23 0.88 52.94 5 4.41 38.55 3.19 44.27 2.51 46.83 1.71 49.84 7.5 5.86 32.94 4.41 39.70 3.55 42.94 2.48 46.95 10 7.01 28.56 5.45 35.80 4.47 39.48 3.20 44.25 12.5 7.95 25.04 6.35 32.43 5.30 36.39 3.88 41.70 15 8.74 22.15 7.14 29.49 6.04 33.59 4.52 39.31

The dried film containing the materials listed above is then rehydrated with aqueous

phosphate buffered saline (PBS) solution (pH 7.4) by sonicating the sample at low

frequency (Hielscher UP200S Ultrasonic Processor, Hielscher Ultrasonics, Teltow,

Germany) for approximately 3 minutes at 20% amplitude. This has the dual effect of 42

dissolving the lipid mixture in solution and raising the temperature above that of the

DSPC gel phase transition temperature, 55 oC. The rehydrated solution is then cooled

and aliquoted out into 2 ml serum vials and sealed. 1.5 ml of the dissolved lipid solution

is added to each vial, as this is determined to be the optimal gas-to-aqueous ratio to result

in the most concentrated microbubble sample.

The head space air is then evacuated from the vial and replaced with the fluorinated

heavy gas, SF6. Finally the vials are vigorously shaken using the Vialmix shaker

(Lantheus Medical Imaging) in order to disperse the gas phase. During this step, the head space gas is broken down into small enough fragments that it will be preferentially coated by the lipid and PEG functionalized lipid. The new lipid/PEG coating stabilizes the microbubble such that it will remain stable even when exposed to the atmosphere for at least 3 days (see Chapter 6 for in depth analysis of contrast agent shelf life). The

resultant microbubbles are allowed to settle at room temperature for 30 minutes; however

long term storage should occurs at 2-8 oC. These techniques successfully produce stable microbubbles with a 1-2 µm diameter.

2.2.3 Microbubble Size Determination

As evident from the oscillatory nature of these microbubbles under a sound field and the

inertial cavitation criteria put forth previously, the resting size of a microbubble is an

important parameter to measure. Microbubbles are difficult to measure with dynamic

light scattering (DLS) as they are on the larger end the acceptable measurement range (10

– 1000 nm), and they do not obey Brownian motion, a necessary criteria for measuring 43

the size. The gold standard for measuring microbubble size distributions is the Coulter

Counter (Beckmann-Coulter, Brea, CA). However, in the absence of such a device and on a budget, microscope image processing techniques can be employed to accurately measure size distributions of microbubbles.

The size distribution of the population of microbubbles was determined by a MATLAB

(Mathworks, Natick, MA) image segmentation program. Samples of the selected shell

compositions are separately prepared by the same method listed above and diluted 10

times to aid the analysis of the program, since overlapping or clustered microbubbles cause anomalous results. First, four images are recorded from each of four samples prepared of a given shell composition (resulting in 16 images per shell composition).

The images are recorded with an optical Carl Zeiss Axioskop 2+ microscope (Carl Zeiss

AM, Oberkochen, Germany). An example of a typical microbubble image (magnified by

a 100X objective) is displayed below in Figure 2.1 for a shell composition of 95 mole%

DPSC, 5 mole% DSPE-PEG 2000.

44

Figure 2.1: Typical microbubble micrograph. This micrograph is a good representation of a typical

microbubble population. This sample has a shell composition of 95 mole% DPSC and 5

mole% DSPE-PEG 2000. The black circles in the plane of view will be the microbubbles

which will be analyzed.

The goal of the image segmentation software is to correctly identify dark circles of any size and measure their diameter. First, the software finds the difference between an image which has microbubbles (sample image), and a reference image taken with the same objective in the presence of just water. In this way, any imperfections in the lens and constant background color can be removed. The program then converts the image into a binary color scheme using threshold manipulation, as well as inverting the colors.

The colors are inverted in order to remove the white halo from the outside of the microbubbles (deemed not to be part of the measurable microbubble). Figure 2.2 shows 45 the inverted binary image displayed in Figure 2.1, where the microbubbles have been converted into the white circles.

Figure 2.2: Inverted binary microbubble micrograph. The micrograph from Figure 2.1 has been

modified using threshold manipulation to convert it to a binary image (black and white only).

Additionally, the image is inverted so that black microbubbles become white domains.

With this image, the program traces the edge of the white domains and fits them with polygons with a shape fitting algorithm. The program then determines the radii by measuring the vertices of the polygons. The polygons themselves are nearly circular and are a very close match to the actual radius of the microbubbles being images. The outlines polygons can be mapped back onto the original image to illustrate this point. In

Figure 2.3 below, the outlines are traced in blue over the original image being analyzed from Figure 2.1. 46

Figure 2.3: Polygon outlined microbubbles. The blue outlines of the polygons built from Figure 2.1 are

overlaid on the original micrograph from Figure 2.2. This image illustrates the accuracy of

the microbubble image segmentation software as the actual edges of the microbubbles are

closely traced by the blue polygons.

The blue polygons here very closely outline the microbubbles from the initial micrograph. The software indentifies all sizes of microbubbles, as long as they have enough contrast to the background media (basically determined by the focus of the microscope). The main drawback of the software is that the microbubbles need to be at a dilution such that microbubbles are not coming into contact with one another, as this can obscure the size results. By indentifying the vertices of the polygons, the program can calculated the diameters of the imaged microbubbles. By employing widely available 47

MATLAB software, this method is cheap and simple procedure for measuring the size distribution of a population of microbubbles.

2.3 Size Distribution

As discussed in the previous section, the size distribution of a population of microbubbles can be determined from an image segmentation technique. In Section 2.2.3, a population of microbubbles with a shell composition of 95 mole% DPSC, 5 mole% DSPE-PEG 2000 is imaged and run processed with MATLAB. From the image generated in Figure 2.3

(along the 15 additional images taken of this shell composition), the microbubble size distribution data can be collected and analyzed. By analyzing 16 separate images, the

program can collect the sizes of over 200 microbubbles per shell composition. A

histogram of the size distribution is then generated for all the microbubbles analyzed for

the aforementioned shell composition, shown in Figure 2.4.

48

Figure 2.4: Size distribution histogram. This histogram describes the size distribution of a population

of over 200 microbubbles analyzed with a shell composition of 95 mole% DPSC and 5

mole% DSPE-PEG 2000. For this population, the mean radius is approximately 1 µm, and

the distribution is nearly Gaussian. However, the histogram contains more microbubbles

larger than the mean than microbubbles smaller than the mean.

The size histogram from this shell composition has a mean radius of about 1 µm and a standard deviation of 1.6 µm. The distribution has one mode and is nearly Gaussian, however with more microbubbles of relatively higher size than of lower size. This process can then be repeated for the entire set of shell compositions described in Table

2.1. The data collected for the mean values of diameter and the respective standard deviations for this set of shell compositions is shown in Figure 2.5.

49

Figure 2.5: Microbubble mean diameter as a function of shell composition. The size distributions of a

set of shell compositions detailed in Table 2.1 is determined with the image segmentation

method. DSPE-PEG compositions of 1, 2.5, 5, 7.5, 10, 12.5, and 15 mole% and PEG

molecular weights of 1000 [x], 2000 [○], 3000 [□], and 5000 [∆] g/mole are studied. The

mean value for the diameter does not significantly change over the span of studied shell

compositions. Additionally, the standard deviations of the size distributions are very large in

comparison to the change in mean diameter.

From Figure 2.5, it is clear the standard deviations in the microbubble size are large (on average 1.5 µm). It is also clear that the average diameter only ranges from about 1 – 1.5

µm, regardless of the shell composition. While it is possible to observe that the mean diameters are increasing with increasing PEG composition, it is not a statistically 50

significant change due to the size of the standard deviation. Therefore, this data shows that the size distribution of a population of microbubbles is largely insensitive to changes in microbubble shell composition (or at least the changes made for this study, systems of

DSPC and 1 – 15 mole%, DSPE-PEG 1000 – 5000 g/mole).

These results are somewhat curious; however, as it might be expected that mean diameter should increase as molecular weight increases from 1000 to 5000. Theoretically, the thickness of the shell could vary to some degree based on the change in molecular weight. The length of one repeat unit of PEG is 3.9 Å [57], and the number of repeat units presented here varies from 22 (for PEG 1000) to 113 (for PEG 5000), assuming the molecular weight of a PEG repeat unit is 44 g/mole. These values amount to a maximum difference of 35 nm between the length contribution of PEG 1000 and PEG 5000. This difference is very small compared to the average diameter of the microbubbles (between

1 and 1.5 µm). Additionally, the length of 35 nm assumes that the chains stand straight up, normal to the monolayer. This is certainly not the case; their geometry is a function of the composition in the monolayer, and therefore the packing density (this conformational change is discussed at length in Chapter 3). It is also possible that the

PEG chains are invisible to the optical microscope, and are therefore neglected by the image segmentation software. It is unlikely that this is the case, but if so a technique which does not use optics to record size would be preferred (like DLS).

As 85 to 99 mole% of the bilayer is comprised of the same material (DSPC) for all the shell compositions studied, these results make sense. Additionally, all shell compositions 51

display the same shape reported for 95 mole% DPSC and 5 mole% DSPE-PEG 2000

sample (monomodal with near-Gaussian profile), but were not included here for brevity.

In fact the resting size of a self assembled microbubble should be generally set by the

Laplace pressure [58]:

2 = 휎 ∆푃 (Equation 2.1) 푅0

where ∆P is equal to the difference in the pressure inside and outside of the bubble at

equilibrium. Because this pressure difference should be constant for a microbubble at

equilibrium, the only factor influencing the shape is the surface tension, σ. As discussed later in Chapter 4 and thoroughly in other works [36, 59], the difference in the surface tension for a bubble at rest (not under ultrasound) between any of the shell compositions described here is negligible. However small the differences in the size distributions may be, the measured distributions will be used in the models presented in the following chapters for accuracy.

2.4 Incorporation into Subsequent Chapters and Conclusion

As mentioned previously, the size distribution of microbubbles is of importance throughout this work. Although the variations in the distributions are small between the different microbubble shell compositions studied, the shape of the distributions as a 52 whole greatly affect microbubble behavior. In Chapter 3, the size distribution of the microbubble populations is shown to influence the speed of the onset of inertial cavitation. In Chapter 5, the size distribution affects the shape the resonance peak of microbubble populations. Additionally, these measured size distributions will be used when simulating theoretical models in order to better describe the experimental data. In these studies, weighed averages of the size distributions will be employed (weighting based on the measurement occurrence fraction at a give radius).

In this chapter, the size distributions of microbubble populations were measured for a set of shell compositions to be used in the remainder of this work. This set of compositions was defined, the microbubble preparation technique was detailed, and novel image segmentation software based in MATLAB for measuring microbubble size distributions was presented. Finally, it is shown that the size distributions of the microbubble samples measured are monomodal and nearly Gaussian, and display statistically insignificant changes between shell compositions. 53

CHAPTER 3: Microbubble Inertial Cavitation Threshold Pressure

3.1 Introduction

While the ultrasound image exceeds other imaging modalities such as X-ray, magnetic resonance imaging (MRI), and computed axial tomography (CAT) in safety, portability, and cost, it lags in image resolution and contrast. One way the ultrasound image quality can be improved during investigation of the blood circulation or perfusion imaging is the use of ultrasound contrast agents. These contrast agents are gas spheres stabilized by a surfactant coating the gas/liquid interface [12, 60, 61]. While air is sometimes used as the gas, a heavier gas can be chosen to maximize the stability of the microbubble in an aqueous environment. These stable gases (most commonly fluorinated compounds) are typically denser, have lower water solubility, and diffuse slower than air [1]. The gas- stabilizing shell can also be made from a variety of materials, including lipids, polymers, fatty acids, and proteins such as albumin [1]. One advantage to using amphiphilic molecules such as phospholipids is their ability to self-assemble around a gas sphere by orienting their hydrophobic tail groups toward the gas and their hydrophilic head groups toward the aqueous media. Along with the surfactant, an additional molecule is often added to the shell to enhance stability. This additional stabilizer is usually a hydrophilic polymer material which has been functionalized, or covalently bonded, to a lipid or fatty acid [26, 62, 63]. Accordingly, the polymer will face radially outward from the gas surface and protrude into the aqueous media. The advantage of this type of polymer is 54 twofold, namely to prevent the coalescence of groups of microbubbles by steric hindrance, and to convey the property of stealth in vivo, so as to avoid elimination by reticuloendothelial phagocytic cells [26].

Recently, attention has turned to the use of microbubbles as possible vehicles for drug delivery. In many of these applications the drug is incorporated into the microbubble shell material [41, 64]. The mechanism of release for these vehicles takes advantage of a microbubble’s acoustic response in the presence of a sound field, better known as cavitation. At relatively low pressure amplitudes, a microbubble will expand and contract in response to the alternating negative and positive pressures to which it is subjected. When these oscillations in microbubble radius can be sustained, the phenomenon is known as stable cavitation. At relatively high pressure amplitudes, however, the microbubble oscillations increase in amplitude and become non-linear; that is, the changes in radius during expansion and contraction are no longer equivalent. At a certain pressure, termed the inertial cavitation threshold pressure, the microbubble becomes sufficiently large during its expansion phase that it implodes and fractures upon the subsequent rarefaction [28, 29, 60, 65]. This implosion associated with inertial cavitation produces a shockwave, a local increase in temperature, and loud broadband noise [28, 63, 66-68]. The temperature increase and shockwave have been shown to cause damage to nearby microstructures, including cells [63, 69]. The mechanical index

(MI) has been defined to assist ultrasound technicians in avoiding unwanted detrimental health effects. The MI is defined as the peak negative pressure (PNP) divided by the square root of the driving frequency of ultrasound (in MPa and MHz, respectively) and is 55

used to quantify the potential danger of an ultrasound scan; in clinical settings the MI

must be maintained below a value of 1.9 [38].

On the other hand, inertial cavitation effects might be beneficial for drug delivery applications [12, 63, 70]. Depending on the application of interest, one may therefore wish to either achieve or to avoid inertial cavitation, and this requires knowledge of the inertial cavitation threshold pressure for a given population of microbubbles. Moreover, this chapter will show that the inertial cavitation threshold will vary with microbubble shell architecture (such as membrane composition and microstructure) and will therefore allow for some degree of control over when a microbubble will undergo inertial cavitation.

It is therefore necessary to understand which physical properties govern the inertial cavitation pressure and how. While the dynamic behavior of a microbubble in the presence of a sound field is well described [28, 67], an experimental inertial cavitation

threshold pressure is not well defined for varying shell composition. A commonly

accepted condition for inertial cavitation is when a microbubble expands to twice its

resting radius during rarefaction, as this equips the microbubble with sufficient kinetic

energy to implode upon contraction [35]. Given that the amplitude of the microbubble oscillations (and cavitation pressure threshold) is governed by microbubble shell elasticity and viscosity, so too then must the inertial cavitation threshold. It is therefore anticipated that changes in microbubble elasticity and viscosity, as accomplished by

changes in shell composition, can be used to set the inertial cavitation threshold. 56

3.2 Inertial Cavitation Detection

3.2.1 Materials

The lipid 1,2-Distearoyl-sn-Glycero-3-Phosphocholine (DSPC) and Polyethylene Glycol

(PEG) functionalized lipid 1,2-Disteroyl-sn-Glycero-3-Phosphoethanolamine-N-

[Methoxy(Polyethyleneglycol)-2000], ammonium salt (DSPE PEG 2000) were purchased

from Avanti Polar Lipids (Alabaster, AL). The 3000 and 5000 molecular weight DSPE

PEG functionalized lipids were also supplied by the above. Sulfur Hexafluoride (SF6)

was purchased from Airgas (Allentown, PA). All other reagents used were of analytical

grade.

3.2.2 Microbubble Preparation

A lipid film containing various mole% of DSPC and a PEG functionalized lipid is

deposited onto a 20 ml scintillation vial from stock solutions dissolved in chloroform by

N2 spin drying followed by 2 hours in vacuum. The dried film is then rehydrated with 5

ml of aqueous phosphate buffered saline (PBS) solution (pH 7.4) by sonicating the

sample (Hielscher UP200S Ultrasonic Processor, Hielscher Ultrasonics, Teltow,

Germany) for approximately 3 minutes at 20% amplitude. This has the dual effect of

dissolving the lipid mixture in solution and raising the temperature above that of the

DSPC gel phase transition temperature, 55 oC. The rehydrated solution is then cooled

and aliquoted out into 2 ml serum vials and sealed. The head space air is then evacuated 57

from the vial and replaced with the fluorinated heavy gas, SF6. Finally the vials are

vigorously shaken using the Vialmix shaker (Lantheus Medical Imaging) in order to

disperse the gas phase. The resultant microbubbles are allowed to settle at room

temperature for 30 minutes, however long term storage should occurs at 2-8 oC. These

techniques successfully produce stable microbubbles with a 1-2 µm diameter. The size

distribution of the population of microbubbles was determined by a MATLAB

(Mathworks, Natick, MA) image segmentation program described in Chapter 2. Samples

of the selected shell compositions are separately prepared by the same method listed above and diluted to aid the analysis of the program, since overlapping or clustered microbubbles cause anomalous results. The program then detects circles imaged by an optical Carl Zeiss Axioskop 2+ microscope (Carl Zeiss AM, Oberkochen, Germany) and reports the diameter distribution of the sample. To limit the size distribution of microbubbles, a sample is centrifuged (Beckman-Coulter Allegra-64R, Palo Alto, CA) at

3600 rpm for 5 minutes, and the liquid phase is collected for testing.

3.2.3 Cavitation Detection Technique

A home-built high voltage pulser, described in previous work [66, 71], is used to drive a

2.25 MHz, 7.5 cm focus ultrasound transducer (Olympus NDT, Waltham MA). Another

2.25 MHz transducer is set at 90o to the transmitter and receives the acoustic response of

a sample insonified by the transmitting transducer, such that the foci of the two

transducers will overlap. The foci of the spherically focused transducers are cigar

shaped, with a 1 mm diameter, shown in the field simulation in Figure 3.1.

58

Figure 3.1: Field simulation of a transducer. An acoustic field simulation from MATLAB for the 2.25

MHz spherically focused (at 7.5 cm) Olympus transducers is displayed. Regions which have

the deepest red are the areas at which the transducers output will be most intense, and blue

areas where the output is the weakest, or non-existent. Both axes describe a distance in space,

and the scales for both are in meters.

If the transducers are positioned at 90o to one another, it is easy to imagine that the cigar shaped foci form a cross, where the overlapping region is a cube with a volume of 1 mm3.

Both transducers are housed within a 15 liter tank filled with de-ionized water, the setup of which is shown in Figure 3.2.

59

Figure 3.2: Cavitation detection experimental set-up. The cavitation detection system consists of two

2.25 MHz spherically focused ultrasound transducers set at 90o relative to each other, one

transmitting and the other used to receive (not drawn to scale). The overlapping focal region

of the transducers is approximately 1 mm3, located within a larger sample chamber (latex cot).

Raw acoustic data is used to generate acoustic spectrograms, and inertial cavitation is detected

by the determination of the amplitude of the phase inverted signal.

The pulser is capable of delivering peak negative pressures of up to 3 MPa, as calibrated using a needle hydrophone [72]. The received signal is filtered to reduce noise by a 5

MHz low pass filter (Minicircuits, Brooklyn NY) and amplified by +26 dB (Panametrics

NDT, Waltham MA) before being digitized by an oscilloscope (Cleverscope Ltd.,

Auckland NZ). The oscilloscope can resolve 100 MHz sample frequency. The schematic is shown in Figure 3.3.

60

T

R +26 dB

5 MHz

Figure 3.3: Cavitation detection schematic. A home built pulser (designed and synthesized by Michał

Mleczko) drives one 2.25 MHz transducer. A second 2.25 MHz transducer receives the

signal, which is then low pass filtered at 5 MHz, amplified by +26 dB, digitized by an

oscilloscope, and recorded by MATLAB. MATLAB also informs the pulser when to pulse,

and the oscilloscope when to receive.

The transmitting transducer creates pulse trains consisting of 4 pulses of 4 cycles each with 80 µs between pulses. Every other pulse is inverted to allow for phase inversion in signal processing. The total experiment consists of 600 pulse trains, which are transmitted at a repetition frequency of 5 Hz. The experiment is repeated for set peak negative pressure amplitudes between 50 kPa and 2 MPa, and for PEG molecular weights between 2000 and 5000 with PEG concentrations ranging between 1 and 15 mole%. The sample chamber consists of a latex cot (Duro-Med Industries, Valencia, CA) positioned so that the overlapping foci are within the cot. Latex is used in order to minimize sound reflection from the walls of the sample chamber. Previously prepared microbubbles are 61 added to the sample chamber such that the dilution is six million times the initial concentration. This dilution is based on the assumption that one billion microbubbles per milliliter exist in the initial microbubble solution, and such that if well mixed one bubble will be sampled in the focus for every six pulse trains. The selection of this dilution is discussed in detail in Section 3.3. The sample chamber is stirred by a magnetic stir plate at 600 rpm set under the tank. For each new pressure amplitude, a fresh concentration of bubbles is added to the sample chamber, and each composition is repeated in triplicate in order to ensure at least one hundred microbubbles are analyzed for statistical significance.

The received signal is then processed by a MATLAB program. For each pulse train collected the program determines first whether a microbubble is found, and secondly if a microbubble is found, whether or not it is destroyed. To determine whether a bubble is found, a phase inversion technique is used where the waveforms from the first and second pulses are added together. Since the waveforms from the first and second pulse are inverse of one another, any linear response will be added to zero. This is the case for the walls of the sample chamber. The responses of the front wall to the first 2 pulses (one positive and one negative 4 cycle sine wave) are shown below in Figure 3.4. As displayed, the responses are equal and opposite for this linear oscillator, and their addition results in zero signal (or just noise).

62

Figure 3.4: Phase inversion technique. The received waveforms of only the response of the front wall

of the latex sample chamber for the first two pulses (first positive [blue], and second negative

[green] 4 cycle sine wave) are displayed. It is easy to see from the graph that the responses of

these pulses are equal in magnitude and opposite in phase, and their sum will equal zero.

Non-linear oscillations, like those given off by cavitating microbubbles, will not be cancelled and show a significant response. The program then determines a median and max value for the addition of the first two pulses. If the max/median of the addition of the first two pulses is greater than the empirically determined detection threshold, than a bubble is determined to be found. To determine whether the bubble was destroyed, the program similarly adds the third and fourth pulses. The addition of the third and fourth pulses is then subtracted from the addition of the first and second pulses. In this way, the program can determine in what condition a bubble found in the first set is in the second set. If this subtraction is greater than the empirically determined destruction threshold, than that bubble is determined to be destroyed. Sample pulse trains which specify both 63 these conditions are shown in the figures below (bubble found and not destroyed in

Figure 3.5, bubble found and destroyed in Figure 3.6).

Figure 3.5: Conditions for an undestroyed microbubble. Acoustic spectrograms (left) and phase

inverted waveforms (right) are displayed for 3 conditions: phase inversion of the first 2 pulses

(top), phase inversion of the second 2 pulses (middle), and the difference between the 2 pulse

sets (bottom). In this example, a microbubble is found in the top row, as well as the second

row; therefore it is automatically determined in the bottom row that the found microbubble

has not been destroyed. Acoustic spectrograms are displayed as a frequency index versus a

time index, and the waveforms are a voltage versus a time index. 64

Figure 3.6: Conditions for a destroyed microbubble. As in Figure 3.5, acoustic spectrograms (left) and

phase inverted waveforms (right) are displayed for 3 conditions: phase inversion of the first 2

pulses (top), phase inversion of the second 2 pulses (middle), and the difference between the 2

pulse sets (bottom). Here, a microbubble is found in the top row, however only noise is

present in the second row; therefore it is automatically determined in the bottom row that the

found microbubble has been destroyed. Acoustic spectrograms are displayed as a frequency

index versus a time index, and the waveforms are a voltage versus a time index.

In each row of the preceding figures, the MATLAB program asks a question. In the first row, it asks whether a microbubble is detected in the focus or not (top row).

Microseconds later, it again asks whether a microbubble is detected (middle row).

Finally, in the last row, the program asks whether a bubble found in the top row has been destroyed in the second row (only if yes to the first question). Both these questions are determined by empirically determined threshold values of the max signal divided by the 65 mean signal of the waveform. In Figures 3.D and 3.E, the max/mean values of each row are displayed above their respective acoustic spectrogram. If the max/mean value of the phase inverted signals (top or middle row) is greater than 10, than a bubble is considered to be found. Additionally, if the difference of the inversions (bottom row) has a max/mean value greater than 7, than the found microbubble is considered to be destroyed. While these values may seem arbitrary, it is clear from the above figures that there exist clear cases of microbubble detection or the lack thereof. Depending on the acoustic pressure, the max/mean values reported for found microbubbles can drop as low at 7.5; however, even at the highest acoustic pressures studied here, the max/mean value for noise (or no microbubble found) never reaches higher than 3.5. Taken together, these results lend credibility to the selection of the max/min threshold values for detection and destruction. This method can generally be referred to as the double passive cavitation identification technique.

To ensure a microbubble cannot travel across the focus during the a single pulse train, the speed of mixing must be set such that a microbubble cannot cross the 1 mm focus within a single pulse train (0.3 ms), but will have sufficient time to clear the focus in the time between pulse trains (0.2 s). The mixing speed is therefore set to 600 rpm (in a 1 cm radius sample chamber, where the bubbles travel rotationally) to ensure the max distance travelled by a microbubble within a single pulse train does not exceed 50 µm, which is far less than the overlapping foci distance of 1 mm. Based on this speed, the bubble can theoretically travel a distance of 125 mm in 0.2 seconds, far greater than the length of the overlapping foci. However, adjacent pulse trains with microbubbles found are excluded 66

from the processing to remove the possibility of the same microbubble being analyzed

twice. In this way the program determines how many microbubbles are destroyed out of

how many microbubbles are detected.

3.3 Microbubble Acoustic Response

The pulser described earlier can also be used to measure the acoustic response of the microbubbles during sonication. To measure the acoustic response, the magnitude of the voltage received by the transducer is analyzed over a period of sonication time. This

method is somewhat more rudimentary than the technique described earlier to measure

inertial cavitation; however it can be used as a tool to define certain parameters of the

experiment. One such parameter is the optimal concentration of microbubbles within the

sample chamber for inertial cavitation detection, discussed in brief in the previous

section. For this study, the concentration of microbubbles can be varied from relatively

low concentrations (20 million times dilutions in PBS) to relatively high concentrations

(up to only 100 times dilution of the initial microbubble formulation). The results of this

dilution experiment, preformed at acoustic pressure of 500 kPa over a period of 140

seconds, are shown in Figure 3.7. The pressure is selected to create a high enough signal

to noise ratio in the microbubble response without destroying an excess of microbubbles.

The time of sonication is selected to match the time of sonication planned for the

cavitation detection study.

67

0.00045

0.0004

0.00035

0.0003 Dilution 0.00025 20 MM 10 MM 0.0002 6 MM Voltage (V) Voltage 3 MM 0.00015 500k

0.0001

0.00005

0 0 20 40 60 80 100 120 140 Time (s)

Figure 3.7: Acoustic response of various microbubble concentrations. The raw acoustic response in

volts of microbubble dilutions of 500k, 3MM, 6MM, 10MM, and 20MM times dilution are

recorded over a period of 140 seconds (or 600 waveforms at 5 Hz pulse repetition frequency).

The higher concentrations – 500k and 3MM times dilution – exhibit multiple scattering

effects at early times. At the lowest concentration – 20MM times dilution – the signal to

noise ratio very low. The intermediate concentrations – 6MM and 10MM times dilution – are

most suitable for the cavitation detection studies.

In the relatively higher concentrations, 500k and 3MM times dilution, the voltage response increases first before decreasing. This is counter intuitive because the acoustic response is expected to decrease as sonication time increases; that is to say, as more microbubbles are being destroyed, the acoustic response of the sample is decreasing.

This initial increase is due to the effects of multiple scattering and the inability of tightly 68

packed microbubbles to oscillate adequately. After a sufficient number of microbubbles

have been destroyed, the acoustic response can then reach its maximum value, and begin

to drop again as more microbubbles are destroyed. This multiple scattering effect is

undesired; especially because it is preferred to only analyze a microbubble during

approximately once every fifth pulse (to avoid measuring the same bubble on multiple occasions). On the other hand, at the lower concentration – 20 MM times dilution –

throughout the experiment the acoustic response barely comes beyond the noise level.

This is simply because such a small amount of microbubbles are being analyzed. For the

purposes of this work, this low concentration is not enough give a sufficient signal to

noise ratio, and does not analyze enough microbubbles over the course of the experiment

to be statistically significant. Therefore, the intermediate concentrations, 6 MM and 10

MM times dilutions, will be adequate for the cavitation detection studies.

Even at these concentrations, there still exist some sequential pulse trains in which a

microbubble is identified by the cavitation software. Analyzing a microbubble in every

waveform is unwanted, as any given microbubble should only be analyzed once. This

concentration theoretically allows a microbubble only to appear in the focus in one of

every six pulse trains. While in practice this is not exactly true, adjacent pulse trains in

which a bubble is detected are discarded to avoid the possibility of recording the response

from the same microbubble.

3.4 Transducer Calibration

69

Before the measurements of microbubble percent destruction can be attempted, it is important to determine at what peak negative pressures (PNP) the microbubbles are experiencing. This is not a simple task however, as the input to the piezoelectric transducer is a set voltage programmed into the pulser (SchaumSchläger). The properties of the transducer material determine how it converts voltage into mechanical vibrations and the sound wave. A hydrophone needle is used measure the acoustic pressure of the sound wave inside the transducer focal region. The hydrophone has a sensitivity of -276 dB re 1 V/µPa at the transducer frequency of 2.25 MHz (as sensitivity is a function of frequency). So to calibrate the transducer, the voltage output of the pulser can be varied between 0 and 255 Volts (peak to peak). The hydrophone, positioned in the transducer focus, picks up the response of the signal (also in voltage), which can then be converted to pressure by the sensitivity. By this method, a curve can be fit to the experimental data to describe the acoustic pressure of any possible voltage input from the pulser. The results of the transducer calibration are shown in Figure 3.8, below.

70

3.5

3

2.5

2

1.5

1 Peak Negative Pressure (MPa)

0.5

0 0 50 100 150 200 250 300 SchaumSchlager Set Voltage (V)

Figure 3.8: 2.25 MHz transducer calibration. The input set voltage of the pulser is converted into

acoustic pressure using a needle hydrophone with a sensitivity of -276 dB re 1 V/µPa at 2.25

MHz. The peak negative pressure of the signal in the transducer focus has a linear region at

low set voltages, then reaches an asymptote at approximately 3.2 MPa. The data is described

by an empirical 4th order polynomial equation which can be used to describe the acoustic

pressure at any pulser set point.

The data above in Figure 3.8 is linear in the region of interest, 0 – 2 MPa (or 0 – 45 set volts). However for future work with the Olympus transducer it is best to characterize the entire range of pulser set voltages with an empirical equation describing the calibration data. The empirical 4th order polynomial equation is listed below for reference in Equation 3.1:

71

-10 4 -6 3 -4 2 -2 -2 PNP = -7.165*10 (Vs ) + 1.016*10 (Vs ) - 3.961*10 (Vs ) + 5.941*10 (Vs) + 4.799*10

(Equation 3.1)

where PNP is the peak negative pressure in MPa, and Vs is pulser set voltage in V. While

Equation 3.1 is purely empirical, it describes the measured data quite well, and has an R² value of 0.998. With this calibration curve and equation, the inertial cavitation behavior of microbubbles can be studied as a function of acoustic peak negative pressure (as well as varying shell composition).

3.5 Cavitation Threshold Pressure as a Function of Shell Composition

This section details the measurement of microbubble cavitation threshold pressures, and the effects of altering microbubble shell composition. Specifically, the microbubble shell composition will be altered by a change in the functionalized PEG mole fraction and molecular weight. The inertial cavitation data as an overall percent of a microbubble population destroyed is reported as a function of increasing peak negative pressure. The percent of microbubbles destroyed divided by total microbubbles measured is determined for each of the samples as described in the previous section. Each sample is sonicated at peak negative pressures of 50, 100, 225, 350, 500, 600, 800, 1000, 1250, 1750, and 2000 kPa. For a given sample, the percentage of destroyed microbubbles was measured, along with 95% confidence intervals for at each of the pressures listed above. Results were plotted in the form of destruction profiles (% destroyed versus peak negative pressure) 72 fitted with a cumulative Gamma distribution. For all samples, the destruction threshold increased sigmoidally similar to Figure 3.9, which gives results for the 1 mole% DSPE

PEG 2000, 99 mole% DSPC system.

Figure 3.9: Representative bubble destruction curve. Graph of percent bubble destruction with

increasing acoustic peak negative pressure (PNP). Results shown are for a contrast agent

consisting of 99 mole% DPSC and 1 mole% DSPE-PEG2000 functionalized lipid. No

cavitation is observed at PNP less than 0.4 MPa, which is defined as the inertial cavitation

threshold value, PT0. PT50 and PT100 are therefore defined as the pressures required to

cavitation 50 and 100 percent of the microbubble population, and for this sample are 0.85

MPa and 1.5 MPa, respectively. Between the measured values, the cavitation destruction

profile is fit with a cumulative Gamma distribution with 95% confidence intervals.

The destruction profiles were used to identify three peak negative pressure thresholds for each sample: PT0, defined as the pressure at which inertial cavitation first occurs, PT50, 73

defined as the pressure which yields 50% fractional destruction, and PT100, defined as the

pressure at which the sample is fully cavitated. For example, in Figure 3.9 the values of

PT0, PT50, and PT100 are 0.4, 0.85, and 1.5 MPa, respectively. The Gamma distribution is simply used as a consistent and unbiased method of providing a smooth curve through and between data points.

Results for tests pertaining to PEG compositions of 1, 2.5, 5, 7.5, and 10 mole% (PEG

molecular weight 2000) are shown together in Figure 3.10A. It is observed that the

microbubbles require higher peak negative pressure to cavitate as the mole fraction of

PEG in the formulation increases (PT50 values of 0.85, 0.88, 0.93, 1.19, and 1.26 MPa are

recorded for PEG concentrations of 1, 2.5, 5, 7.5 and 10 mole%, respectively). This trend

also holds when the PEG molecular weight is changed to 3000 and 5000 (Figure 3.10B,

C, respectively).

A

74

B

C

Figure 3.10: Influence of PEG molecular weight and composition on cavitation thresholds. Graphs

report percent bubble destruction with increasing acoustic peak negative pressure. Systems

include: A DPSC/DSPE-PEG2000 system containing DSPE-PEG2000 concentrations of 1,

2.5, 5, 7.5, 10 mole%, with acoustic pressure ranging from 50 kPa to 2 MPa. The data is fit

to a cumulative Gamma distribution with 95% confidence intervals. The varying

concentrations of PEG all exhibit the same increasing sigmoidal trend with increasing

acoustic pressure. However, as the concentration of PEG increases, more pressure is 75

needed to cavitate a similar fraction of microbubbles. B DSPC/DSPE-PEG3000 system

containing DSPE-PEG3000 concentrations of 1, 2.5, 5, 7.5, 10 mole%. Similar trends to

Figure 3.10 A are observed. C DSPC/DSPE-PEG5000 system containing DSPE-PEG5000

concentrations of 1, 2.5, 5, 7.5, 10 mole%. Similar trends to Figure 3.10 A, B are observed.

As with Figure 3.9, the results of Figure 3.10A-C were used to identify PT0, PT50, and

PT100 values for each sample. Figure 3.11 shows how PT50 varies with PEG mole fraction

for each of the PEG molecular weights used. Here, one notes a slight decrease in PT50 for

increasing PEG molecular weight. The vertical dashed lines at 4 and 8 mole% represent

literature values corresponding to phospholipid membrane phase behavior. 4 mole%

represents the mole fraction of PEG-lipid where the surface phase changes from

mushroom regime to brush regime, and 8 mole% corresponds to the PEG-lipid saturation

limit in a lipid membrane (for PEG 2000) [26, 73, 74]. Changes in PEG molecular weight shift these transitions slightly.

76

Figure 3.11: PT50 cavitation pressure dependence on PEG molecular weight and composition. The

mean cavitation threshold pressure, or PT50, is plotted for each of the systems in Figure 3.10

A, B, C against the concentration of their respective molecular weights of PEG. Each of

the three molecular weights of PEG (2000[♦], 3000[■], and 5000[▲]) show a sigmoidal

increase in inertial cavitation pressure as the concentration of PEG increases. The

inflection points of each molecular weight are at approximately 4 mole% and 8 mole%.

Additionally, as molecular weight of PEG is increased, the mean cavitation threshold

pressure decreases slightly. The transition at around 4 mole% is reported in literature as the

point at which lipid functionalized PEG transitions from the mushroom configuration phase

to the brush configuration phase. The transition at 8 mole% is also reported in literature as

the composition at which PEG-lipid membranes are saturated with functionalized PEG [26,

73, 74].

To attempt to identify the cause of the change in cavitation threshold pressure, the resting microbubble size of all the samples was also measured. Figure 3.12 B shows a sample size distribution for a population of microbubbles from the 90 mole% DSPC / 10 mole%

DSPE-PEG2000 system. A destruction curve for this population is measured, and then the population is the centrifuged to limit size polydispersity. The centrifuged sample size distribution is presented in Figure 3.12 C. Before centrifugation the mean microbubble radius is 0.71 µm, and the variance of the radii is 0.122 µm; after centrifugation the mean radius is 0.49 µm, with a variance of 0.052 µm. Figure 3.12 A shows the comparison of the destruction curves for the sample before and after centrifugation.

77

Figure 3.12: Cavitation threshold variance as a function of microbubble size polydispersity for the

90 mole% DSPC / 10 mole% DSPE-PEG2000 system. A Cavitation destruction curves

for two different populations of microbubbles. The steeper curve belongs to a population

which is centrifuged at 3600 rpm for 5 minutes (○) and the more gradual curve to a freshly

prepared sample of microbubbles (x). The value of PT50 for both curves is the same for both

populations, 1.2 MPa. The size distributions from the two populations are shown: B The 78

size distribution of a freshly produced population of microbubbles. The mean radius is 0.71

µm +/- 0.35 µm. C The size distribution for the same sample in Figure 3.12 B after

centrifugation. The mean radius is 0.49 µm +/- 0.22 µm.

The onset of cavitation in the centrifuged sample is much more sudden than before

centrifugation, and the curves intersect at their PT50 values. A comprehensive study of the resting diameter distribution as a function of PEG composition and molecular weight is described in Chapter 2. The microbubble size shows no statistically significant change throughout the samples. The size distribution is fairly constant between 0.5 and 2.5 µm,

with a mean diameter of approximately 1 µm.

3.6 Simulating Inertial Cavitation Thresholds

To add to the credibility of the measured cavitation threshold values, the experimental

behavior is compared with simulated predictions. These predictions consist of solving

the modified version of the Herring equation (itself a modification of the well-known

Rayleigh-Plesset equation (Equation 1.17)) [75], which describes pressure amplitude as a

function of microbubble resting radius, to find the pressure amplitude which satisfies the

criteria for cavitation at a given microbubble resting radius. Since the microbubbles used

in this work are not monodisperse in radius, the theoretical threshold pressure calculated

as a function of resting radius is superimposed onto the measures size distributions.

Then, for each experimental pressure tested, the fraction of microbubbles whose radii

correspond to a pressure threshold less than the applied (experimental) pressure is 79

identified. The microbubble fractions identified in this fashion serves as the prediction for comparison with the measured microbubbles destruction profiles.

3.6.1 The Herring Equation

Conyers Herring was an American physicist working with the National Defense Research

Committee (NDRC) during the Second World War. Herring’s work to this point had little to do with microbubble cavitation phenomenon (in fact it was in solid state physics), until he was assigned to the subsurface warfare division of the NRDC, and he was forced to take a closer look at Lord Rayleigh’s work. In 1941, Herring made his modification to

Rayleigh’s equation [76], which consisted of taking into account that the surrounding fluid is not completely incompressible by adding an extra term to Equation 1.12:

3 1 + = ( ) + 2 2 푹 푅푅̈ 푅̇ �푃퐿 − 푃0 − 푃 푡 푷푳̇ � 휌 풄 (Equation 3.2)

where c is the speed of sound in the surrounding liquid and is the first derivative of the

퐿 pressure outside the bubble with respect to time (also note this푃̇ equation does not include

Poritsky’s viscous damping term as Herring’s work was 10 years its prior). Since PL is

described previously in Equation 1.16, its derivative can be taken and rearranged to give:

1 2 2 = 3 + 3훾 + 0 ̇ 퐿 0 휎 푅 휎푅 푃̇ �− 훾푅̇ �푃 0� � � � 푅 푅 푅 푅 (Equation 3.3) 80

Therefore substituting Equation 3.2 into Equation 3.3 yields the final version of the

Herring equation [76] (with some algebraic rearrangement and the addition of Poritsky’s

viscous damping term, for posterity).

3 1 2 3 2 4 + = + 1 1 ( ) 2 3훾 2 휎 푅0 훾푅̇ 휎 푅̇ 휇푅̇ 푅푅̈ 푅̇ ��푃0 � � � � − � − � − � − − 푃0 − 푃 푡 � 휌 푅0 푅 푐 푅 푐 푅 (Equation 3.4)

3.6.2 Morgan’s Modification of the Herring Equation

Since the development of equations like the RPNNP and Herring’s equation, many subsequent modifications have been made to both, especially towards incorporating the effect of the microbubble surfactant shell. Karen Morgan has made one such modification famous in 2001 by adding shell properties into the derivation of Herring’s equation [54]. Specifically, Morgan added the effects of the elastic modulus and shell viscosity into the Herring equation. The addition of shell material properties such as these is of interest to this study because such parameters are needed to better describe the changes in the microbubble shell composition. The Morgan model is therefore selected to simulate the cavitation destruction profiles, with the shell properties mentioned above as tuning parameters. The Morgan modification of the Herring equation [54] is shown below in Equation 3.5:

81

3 1 2 2 3 2 4 + = + + 1 1 2 3훾 2 휎 휒 푅0 훾푅̇ 휎 푅̇ 휇푅̇ 푅푅̈ 푅̇ ��푃0 � � � � − � − � − � − 휌 푅0 푅0 푅 푐 푅 푐 푅 2 3 1 12 ( ) 2 ( ) 휒 푅0 푅̇ 푅̇ − � � � − � − 휇푠ℎ휀 − 푃0 − 푃 푡 � 푅 푅 푐 푅 푅 − 휀 Equation 3.5

where R is the instantaneous radius of the bubble, and are the first and second

derivative of the bubble radius with respect to time, ρ푅 ̇ is the 푅densitÿ of the surrounding

media, P0 is the hydrostatic pressure, σ is the interfacial tension, Ro is the mean

microbubble resting radius, χ is the shell elastic modulus, γ is the polytropic gas constant,

c is the outside media speed of sound, µ is the viscosity of outside media, µsh is the shell

viscosity, ε is the shell thickness, and P(t) is the driving pressure function (the same

shape as previously defined). The values for ρ, P0, σ, γ, µ, and c will be constant for a system of invariable shell lipid, encapsulated gas, and surrounding media. However, the interest of this study will be to vary the relevant shell material properties, χ and µsh.

The Morgan modification of the Herring equation can be solved numerically to determine

a cavitation threshold curve with respect to resting radius. In this way, the amplitude of

P(t) is increased and the Morgan equation is differentially solved for R until the

amplitude which gives R = 2R0 with the given parameters is located, where 2R0 is an

acceptable estimate of the size a microbubble must reach for it to inertially cavitate [70,

77]. R0 is then increased iteratively and the process of finding the amplitude of P(t) which gives R = 2R0 is repeated for each new R0. The peak negative pressure of P(t) 82

which solved the equation is plotted against their respective R0 steps to create a cavitation

threshold plot. The lowest trough of this pressure curve is known as the optimal size and

pressure for bubble cavitation [38, 65]. Overlaid with this pressure curve is the measured

size distribution of the shell compositions analyzed. This is necessary to take into

account the range of microbubble sizes found in order to analyze a real sample with a

polydisperse population, which will correspond to a distribution of cavitation pressures.

Therefore, to generate a plot of fraction of bubbles destroyed, steps of pressure are

iterated to determine what percentage of the overall occurrence of the overlaid size

distribution is above the pressure curve. The percentage of the size distribution is

therefore correlated to the fraction of microbubbles destroyed at its respective pressure.

In this way, by altering shell viscosity and elasticity parameters within physically

relevant ranges, the experimental results can be fit with a theoretical comparison based on

the Morgan modification of the Herring equation.

Therefore, the experimental data recorded in Figure 3.10 A-C is modeled with the

Morgan modification of the Herring Equation. Again, the interest of this study lies in altering shell material properties to model its behavior and thus χ and µsh will be

variables, while the other parameters listed in Table 3.1 will be constant.

Table 3.1: Modified Herring equation model parameters.

Hydrostatic pressure P0 10130 Pa

Resting radius R0 1 µm

Media density ρ 998 kg m-3 83

Interfacial tension coefficient σ 0.051 N m-1

Polytropic gas exponent γ 1.07

Speed of sound in media c 1500 m s-1

Media viscosity µ 0.001 Pa s

Shell thickness ε 1 nm

For the purposes of this study, the pressure function will be a single 4 cycle sine wave, displayed in Chapter 1. The Herring equation is then numerically solved for R and the amplitude of the 4 cycle sine wave in P(t) is increased incrementally until the amplitude value which results in R = 2R0 is found. R0 is then increased iteratively from 0.1 µm to 3

µm in steps of 0.1 µm, and the process of finding the amplitude of P(t) which gives R =

2R0 is repeated for each new R0. The peak negative pressure of P(t) which solved the equation will be plotted against their respective R0 solutions to create a cavitation threshold plot, an example of which is given in Figure 3.13.

84

Figure 3.13: Herring equation optimal cavitation size. Graph of the theoretical cavitation pressure

and relative occurrence related to resting radius of microbubbles. The Morgan solution

pressure curve is generated by solving the Morgan modification of the Herring equation at a

range of amplitudes of the pressure function for the point when the instantaneous radius is

equal to 2 times the resting radius (solid line). The lowest point on the pressure curve is

related to the optimum resting radius for microbubble cavitation. The size distribution for a

population of microbubbles comprised of 99 % mol DSPC and 1 % mol DSPE-PEG2000 is

overlaid (dashed line).

Also overlaid in Figure 3.13 is a sample size distribution measured earlier for each of the shell compositions analyzed. Now it is of interest to generate the sigmoidal curve of fraction of bubbles destroyed against increasing peak negative pressure. To accomplish this, steps of pressure are taken to determine what percentage of the overall occurrence of the size distribution is above the Morgan equation curve at a given pressure. This percentage above the curve is therefore correlated to the fraction of microbubbles 85 destroyed in the measured cavitation threshold destruction curves and overlaid in the results (example in Figure 3.14).

Figure 3.14: Theoretical Herring model comparison with experimental data. A sample of the

modified Herring equation theoretical model (x line) compared to experimental results

(solid line) from a cavitation experiment of the 90 % mol DSPC, 10 % mol DSPE-

PEG2000. The theoretical model displayed was created using the parameters in Table 1,

-1 and with χ = 6 N m , µsh = 4 Pa s.

-1 In this way the shell material properties can be altered; χ between 1-13 N m , and µsh between 0.1-5 Pa s to match the experimental results with a theoretical model based on the Morgan modification of the Herring equation. The range of relevant χ and µsh values are plotted as theoretical fractional destruction as a function of peak negative pressure in the sensitivity plot shown in Figure 3.15.

86

Figure 3.15: Range of relevant χ and µsh values. Graph shows of the range of theoretical values of the

-1 elastic modulus (χ) in N m and the shell viscosity (µsh) in Pa s. The cavitation destruction

curves show that the fraction destroyed decrease with increasing χ and µsh at a single

pressure. The graph was built with the following data sets (in descending order): χ=1,

-1 µsh=1; χ=5, µsh=1; χ=5, µsh=5; χ=10, µsh=1; χ=10, µsh=5; and χ=10, µsh=10 [N m , Pa s].

Taking this sensitivity study a step further, theoretical cavitation profiles can be

determined in this manner for a large range of input parameters, χ and µsh. For the purposes of this study, the input parameters will range from 0 – 8 N/m in elastic modulus, and 0 – 8 Pa s in shell viscosity. Although this is a rather large range (especially in shell viscosity), this should provide a better picture of how the cavitation threshold theoretically changes with material parameter alterations. Figure 3.16 displays all the theoretically calculated inertial cavitation thresholds (PT) as a function of the input

parameters entered into the Morgan’s modification of the Herring equation used to solve

for the cavitation threshold. 87

Figure 3.16: Theoretically determined inertial cavitation thresholds. Theoretical inertial cavitation

thresholds displayed here are calculated using Morgan’s modification of the Herring

equation (Equation 3.5) using a range of input parameters – shell viscosities of 0 – 8 Pa s,

and elastic modulus of 0 – 8 N/m. In general, increasing the shell viscosity drastically

increases the cavitation threshold pressure, and increasing the elastic modulus slightly

increases the cavitation threshold pressure.

Figure 3.16 shows that the cavitation threshold pressure increases with both increasing shell viscosity and elastic modulus. Both of these effects stiffen the membrane, which subsequently will cause the microbubble to require more pressure to inertially cavitate.

While all these theoretical cavitation thresholds are correct for the given input parameters, it is desirable to find which set or sets of input parameters determine the 88

cavitation threshold pressure which most closely matches the measured cavitation

thresholds.

To solve this problem, not only the values of inertial cavitation threshold pressure, but the

shape of the modeled and measured cavitation profiles should be compared. In addition

to the model determining the cavitation threshold pressure for each set of input

parameters, it also builds theoretical cavitation profiles, an example of which is shown in

Figure 3.14. A simple Cartesian norm is applied to find the difference in the shapes of

the modeled and measured curves:

= ( ) + ( ) + 2 2 푒 �� 퐹푡푖 − 퐹푒푖 퐹푡푖+1 − 퐹푒푖+1 ⋯ (Equation 3.6)

where e is the error between the measured and modeled cavitation profiles, Ft is the fraction destroyed at a given pressure from the theoretical cavitation profile, and Fe is the

fraction destroyed at a given pressure from the measured cavitation profile. For a given

shell composition system, the squared error between the modeled cavitation profiles and

a single experimental profile (for the given system) is calculated and plotted as a function

of the input parameters in Figure 3.17. Because a two parameter fit is employed in

solving Morgan’s modification of the Herring equation, a unique solution does not exist.

In fact, there exists a line of input parameters that will satisfy the criteria for matching the

modeled and measures inertial cavitation thresholds. Figure 3.17 shows the squared error 89 results for a shell composition comprised of 99 mole% DSPC and 1 mole% DSPE-

PEG2000.

Figure 3.17: Error surface for a given shell composition. The graph displays the values of the squared

error (calculated from Equation 3.6) as a function of the input parameters (0 – 8 Pa s in

shell viscosity, and 0 – 8 N/m in elastic modulus) for a microbubble population comprised

of 99 mole% DSPC, 1 mole% DSPE-PEG 2000. The lowest values of the squared error are

tied to the input parameters which give the best agreement between the modeled and

measured cavitation profiles, represented in this figure by the solid pink line.

90

For each shell composition, an error surface like the one displayed in Figure 3.17 can be computed. In this error surface, the values of the input parameters which have the lowest error value between measured and modeled are highlighted in pink. For this shell composition, the pink line therefore represents the best fit input parameters for the

Morgan modification of the Herring equation. Extending this technique to other PEG mole fractions in the PEG 2000 set, a plane of best fit input parameters can be built. This plane can be assembled simply by calculating the best fit lines for each of the PEG mole fractions (2.5, 5, 7.5, and 10 mole%), and interpolating between the lines in the input parameter space. This plane of best fit input parameters is displayed below in Figure

3.18 for systems of varying compositions of DSPC and DSPE-PEG 2000.

91

Figure 3.18: Plane of best fit input parameters. Lines of best fit input parameters for PEG 2000

compositions of 2.5, 5, 7.5, and 10 mole% (remainder DSPC) are plotted together. The

input parameter space between the measured PEG compositions is interpolated with least

squares. As PEG 2000 composition increases, shell viscosity and elastic modulus increases

(while holding the other respective input parameter constant).

The plane in Figure 3.17 is created using least squares interpolation. The best fit plane also provides some insight into behavior of the input parameters as a function of microbubble shell composition. As PEG 2000 composition increases in the monolayer, so do the values of both shell viscosity and elastic modulus (if the other parameter is held constant). This plane successfully predicts the values of the selected input parameters, shell viscosity and elastic modulus, for any composition of DSPC / DSPE-PEG 2000 microbubbles. Additionally, this plane can be reproduced for any microbubble composition system simply by inputting the measured inertial cavitation thresholds.

3.7 Conclusions

The results of this work show unequivocally that the microbubble inertial cavitation threshold is sensitive to changes in microbubble shell composition. This is not surprising, but until now the result has not been demonstrated for the given systems experimentally. Perhaps more importantly, the results are well-described by a model that quantifies cavitation in terms of rigorous membrane properties, name elasticity and shell viscosity. Accordingly, this work suggests that using shell composition to tune the 92 microbubble inertial cavitation pressure to a desired value is feasible in the range 0.76 –

1.26 MPa.

The ability to tune the microbubble inertial cavitation threshold is of potential significance, given the importance of cavitation concerning safety during imaging. That is, by tuning the inertial cavitation pressure to a relatively high value, one could improve the safety of an ultrasound contrast agent formulation without compromising performance. Moreover, it is likely that tuning the microbubble cavitation pressure could improve efficacy in applications involving microbubbles as actuators or delivery vehicles as occurs in sonoporation and drug/gene delivery.

Taking full advantage of microbubble cavitation threshold tunability requires a solid understanding of the extent to which various physical properties influence the threshold value. Several aspects of this work therefore warrant further discussion. First is the fact that all destruction profiles generated exhibit a sigmoid shape. This is simply due to the fact that the microbubbles used here were not monodisperse, which is true for nearly all microbubble samples, including commercial formulations. The only reported monodisperse microbubble formulations reported are those prepared by microfluidic techniques [78]. For a monodisperse microbubble population, one would expect the destruction profile to exhibit step change. That is, one would expect a single threshold pressure, below which no microbubbles cavitate inertially and above which all microbubbles cavitate inertially. The fact that the percentage of microbubbles undergoing inertial cavitation rises gradually with pressure reflects the polydispersity of 93

the samples. Figure 3.12 demonstrates this effect clearly; centrifuging a formulation

therefore decreases the polydispersity significantly from a variance of 0.122 to 0.052 µm,

leading to a much sharper transition. Accordingly, the polydispersity should be borne in

mind when discussing cavitation thresholds. It should be further noted that the

polydispersity just mentioned relates primarily to the sizes of microbubbles rather than to

any variations in shell composition. A natural question then arises, namely what is the

influence of size on the cavitation threshold? In other words, if the size polydispersity is

what accounts for the breadth in cavitation observed at a given shell composition, then

could changes in size be what causes the observed shifts in the overall destruction profiles as one changes shell composition? The short answer is no; size polydispersity affects the breadth of a given microbubble destruction profile but does not account for shifts in destruction profiles among samples. This is demonstrated clearly by Figure 2.5,

which shows that microbubble sizes are largely insensitive to the various shell

compositions used herein. Thus, the observed changes in cavitation threshold must be

due to some feature of the microbubble other than size that is sensitive to compositional

changes.

The obvious candidate is the shell membrane physical properties. Evidence supporting this view is the result obtained when the cavitation data is plotted as threshold pressure

versus PEG mole fraction for each of the three PEG molecular weighs used. The

threshold pressure is largely insensitive to PEG compositional changes until a mole

fraction of approximately 4.5 mole%, a value which coincides with the published transition of PEG 2000 from a so-called mushroom to a brush configuration, shown in 94

Figure 3.11. Above this transitional composition, the threshold rises sharply with

additional PEG. The cavitation threshold becomes insensitive to PEG composition once

again above approximately 8 mole%, a value which corresponds to the published

saturation value of PEG 2000 in PEG-lipid membranes [26, 73, 74]. At mole fractions exceeding the saturation limit, excess PEG functionalized lipids are thought to self- assemble into micellar structures, which would not be echogenic or detected by the pulse inversion technique applied in this study [79, 80]. Thus, the cavitation results correlate well with known lipid membrane phase behavior. Moreover, these results occur irrespective of the PEG molecular weight used. On the other hand, the PEG molecular weight does influence only the extent of cavitation achieved in the various regions of composition space. Taken together, these results point to change in membrane stiffness as the primary parameter controlling the inertial cavitation threshold.

To test this idea, a well-known model that accounts for microbubble shell stiffness in the presence of a sound field is invoked, namely the Morgan modification of the Herring equation. This model explicitly accounts for two properties of the shell, namely the shell viscosity and the elastic modulus, and describes dynamic microbubble radius as a function of applied pressure. However, the equation does not explicitly identify an inertial cavitation pressure. The approach was to invoke a commonly used criterion for cavitation put forth by Leighton [35], namely that the microbubble must expand to twice its resting radius during rarefaction so as to possess sufficient kinetic energy to implode on the successive contraction. Solving the Morgan modification of the Herring equation for this criterion gives the expected pressure for inertial cavitation for a given resting 95

microbubble radius. Given the aforementioned size polydispersity of the samples, the

solution as a function of microbubble radius can be coupled with the measured resting

radii for the samples so as to give predicted destruction profiles. Strictly speaking, the

predictions are not best fits of the data (as this would require computation beyond the

scope of this study); nevertheless, the model predictions agree with the experimental

results using reasonable values of membrane elasticity and viscosity. The values

presented of the elasticity and shell viscosity are examples of a set of parameters which

fit the experimental data, however they are not unique solutions, and for this reason a

range of values are presented in Figure 3.15. It is therefore concluded that the tunability

of microbubble inertial cavitation thresholds has been experimentally demonstrated using

shell composition and that experimental results agree with a well established model of

microbubble physics.

The sensitivity of inertial cavitation threshold to changes in shell viscosity and elasticity

makes shell composition (here, polyethylene glycol (PEG) molecular weight and

composition) a potential tuning parameter for microbubble-based ultrasound contrast and

drug delivery applications. Microbubble shell composition can be used to adjust the

inertial cavitation threshold so as to either avoid or achieve cavitation at a given operating

pressure. This idea was tested by measuring the inertial cavitation threshold for populations of phospholipid-shelled microbubbles suspended in aqueous media, and using this method to quantify the influence of shell composition on the inertial cavitation threshold. The experimental cavitation data was fit with Morgan’s modification of the

Herring equation, using shell viscosity and elastic modulus as the tuning parameters. In 96

conclusion, the design and synthesis of microbubbles with a prescribed inertial cavitation threshold is feasible using PEG molecular weight and mole fraction as tuning parameters. 97

CHAPTER 4: Colloidal Model for Microbubble Oscillations

Since Lord Rayleigh’s derivation of his famous equation, many modifications have been

made to improve the accuracy of the model for predicting microbubble oscillations. For

example, Poritsky famously accounted for the viscous losses to the surrounding fluid to

be included as the last ‘P’ in the RPNNP (designation by Lauterborn [44]); and Herring accounted for the compressibility in the surrounding liquid by adding the mach number

. Since then, many subsequent additions have been made to the Rayleigh’s equation, 푅̇ 푐 �most� of which incorporating Poritsky’s (RPNNP-like) or Herring’s modification, or both.

All of these modifications can trace their derivation to the addition of a term into energy

balance, which Rayleigh initially stated as the work of the expanding bubble is equal to

the kinetic energy of the fluid is it pushing away. In this section, some of the more

famous modifications are examined and their influence on theoretical microbubble

oscillations is displayed.

4.1 Significant Microbubble Dynamics Models

4.1.1 Naked Microbubble Models

Naked microbubbles, or microbubbles without a surfactant shell, were the main focus of

most of the research up until the 1980s and 1990s. This includes the most famous of

these equations, the RPNNP equation (Equation 1.18), along with the Herring equation 98

(Equation 3.4). Note that Equation 3.4 is actually the ‘modified’ Herring equation as

Poritsky’s viscous losses term has been added to it in order to show the progression of the equation from its inception by Lord Rayleigh.

At low acoustic pressures (and therefore small oscillations), both the RPNNP and the modified Herring equation behave similarly. This is because both equations are identical with the exception of Herring’s addition of terms including 1 minus the Mach number.

When the microbubble oscillations are small, the wall velocity ( ) is much smaller than

the speed of sound in the liquid (c), and thus the term approaches푅 unity.̇ However, as the

acoustic pressure is increased above 100 kPa, the difference in the equations is very

noticeable. Figure 4.1 shows the response of the microbubble (both both in non-

dimensional radius and Mach number) predicted by both naked models at two acoustic

pressures, 50 kPa and 200 kPa (with the shape of the 4 cycle pulse shown earlier in

Figure 1.13).

99

Figure 4.1: RPNNP and modified Herring model comparisons. The RPNNP model (black line) and

modified Herring model (blue line) simulations are compared. The simulations in the first

column have an incident pressure of 50 kPa, and the second column has an incident pressure

of 200 kPa. The first row displays the response of the non-dimensional radius (R/R0) and the

second row displays the response of the non-dimensional wall velocity (or Mach number; ( /

)). 푅̇

푐

In the top row of Figure 4.1, the non-dimensional radius response, it is observed that at the low pressure (50 kPa), there exists almost no difference between the RPNNP and modified Herring models. However, as the pressure increases (to 200 kPa) these differences become more pronounced; the modified Herring equation successfully dampens the microbubble oscillations, while the RPNNP predicts unstable oscillations with a maximum R/R0 of 4 (far greater than predicted cavitation thresholds). The same 100 phenomenon is noticed in the Mach number plots, where the speed of the microbubble wall quickly becomes much larger than the speed of sound in the RPNNP predication as the pressure is increased.

If the pressure is increased even more than displayed here (to values above 500 kPa), both models become unstable. It is accepted that models like these can only approximate very small microbubble oscillations. Additionally, neither of these equations have accounted for the possibility of a microbubble shell, as this would not have been of interest in the 1950s when both these researchers were interested in underwater bubbles.

This is no longer the case, as modelers have taken an interest in predicting the behavior of ultrasound contrast agents.

4.1.2 Thinly Shelled Microbubble Models

Since the mid 1980s and the inception of the ultrasound contrast agent, microbubble models have begun to attempt to understand the response of shelled microbubbles. As before, these models add additional damping terms into the energy balance in order to explain the effect of the shell on microbubble oscillations. The following section will analyze three of such equations which make modifications to the RPNNP or Herring.

Although there are many more models which describe microbubble oscillations for both shelled and shell-less systems, these three models are selected because they will help to explain the justification for the presented colloid model for microbubble oscillation described in Section 4.2. One of the first of these modifications was made by Nico de

Jong in 1994 [81], where the shell stiffness parameter (Sp) is taken into effect. 101

4.1.2.1 de Jong Model

de Jong’s modification to the RPNNP was simply to add the effect of the stiffness of the shell into the energy balance by introducing the shell stiff parameter (Sp). Although the

shell stiffness parameter is empirical and mainly used in fitting, it is the first important

step in accounting for the stiffness of the microbubble shell. Note that the de Jong model

has an extra term which describes the overall damping of the system from a variety of

media, δ (viscous, acoustic, and thermal). These damping effects were originally

proposed by Eatock and Nishi in 1984 [82], but their equation is not included here for the sake of brevity. The Eatock and Nishi modification is simply the RPNNP with the addition of the damping term: . As it is cumbersome to express these models in

terms of all of their modifiers,− this훿휔휌푅 work푅̇ names them by their final editor (i.e. de Jong’s

model is really de Jong’s modification of Eatock and Nishi’s modification of Poritsky’s

modification of Rayleigh’s equation). Modifications beyond the Herring or RPNNP

equations will be displayed in bold. The de Jong model can be written as [1, 81]:

3 1 2 2 4 + = + 2 3훾 2 휎 푅0 휎 휇푅̇ ퟏ ퟏ 푅푅̈ 푅̇ ��푃0 � � � − − − 휹흎흆푹푹̇ − ퟐ푺풑 � − � − 푃0 휌 푅0 푅 푅 푅 푹ퟎ 푹 ( )

− 푃 푡 � (Equation 4.1)

102

where δ is the total damping, ω is the center frequency, and Sp is the shell stiffness

parameter. de Jong’s addition of the all encompassing Sp parameter was the first step in

the development of a shelled microbubble model, although this is not a well defined

parameter, and is often cited as being set to values of 1 – 5 N/m [28, 63, 70, 81]. A more

rigorous model defining microbubble oscillations would include one or more well

defined shell material properties, as can be seen in the following sections. However, to

show the initial difference between a naked microbubble model and a thinly shelled

microbubble model, Figure 4.2 displays the response of a microbubble to the same

incident sound wave as in Figure 4.1, at pressure of 50 and 200 kPa. The microbubble is

modeled using both the de Jong equation (red line) and its predecessor, the RPNNP

equation (again, black line) for both its normalized radius and wall velocity. As before,

the following constants are used for a microbubble in an aqueous environment: ρ is 998

kg/m3, P0 is 10.13 kPa, σ is 0.051 N/m, γ is 1.07, µ is 0.001 Pa s, and R0 is 1 µm.

Additionally, the de Jong’s equation parameters are: ω is 2.25 MHz, Sp is 1 N/m, and δ is

0.06 (as from his works and that derived from Medwin [10, 81]).

103

Figure 4.2: RPNNP and de Jong model comparison. The predictions of microbubble dynamic radius

and wall velocity are simulated using both the RPNNP (again, black line) and de Jong’s

model (red lines). The simulations in the first column have an incident pressure of 50 kPa,

and the second column has an incident pressure of 200 kPa. The first row displays the

response of the non-dimensional radius (R/R0) and the second row displays the response of

the non-dimensional wall velocity (or Mach number; ( / )).

푅̇ 푐

The de Jong model predicts oscillations of a lower magnitude than the RPNNP. This is to be expected as the Eatock damping term and shell stiffness term both increase the resistance of the microbubble to oscillation. These modification terms, along with any other credible additions to naked microbubble models, serve to increase the damping of the system and decrease the magnitude of the oscillations. However, the weakness of the de Jong model is in characterizing the shell with the shell stiffness parameter, a fitting 104 parameter which has no value in a predictive model. Future models would attempt to expound on this by introducing rigorously defined physical properties instead of the shell stiffness parameter.

4.1.2.2 Morgan Model

Karen Morgan’s modification of the shelled microbubble oscillation equation contains the terms derived by both Poritsky and Herring [49, 54, 76]. The Morgan equation is used to simulate the cavitation profiles and attempt to explain the experimental cavitation results in Chapter 3, and is displayed in Equation 3.5. This model, derived in 2000, is a significant advance in microbubble physics as it incorporates well defined material properties of the shell, the elastic modulus (χ) and shell viscosity (µsh), as opposed to de

Jong’s fitting parameter, Sp.

Again, Morgan’s equation includes the addition of terms which describe the shell and serve to dampen the oscillations of the bubble. Since the Morgan equation represents an even more stable example of a microbubble dynamics model, its response to the incident sound wave should be examined at even higher pressure amplitudes. Figure 4.3 shows the response of a microbubble’s non-dimensional radius to incident pressure amplitudes of 50, 200, 500, and 1000 kPa. The oscillations become increasingly non-linear as the incident pressure amplitude increases, as well as becoming greater in magnitude. The magnitude of the oscillations varies from 1.07 to 7.5 between 50 kPa and 1 MPa. In these simulations, χ and µsh are constant at 1 N/m and 0.63 Pa s, respectively.

105

Figure 4.3: Morgan model predictions. The predictions of microbubble non-dimensional radius are

simulated using for the Morgan model at four pressure amplitudes. The simulations have

incident pressure amplitudes (top left to right) or 50, 200, 500, and 1000 kPa. In general, the

oscillations grow larger and more non-linear as the pressure is increased.

Observing the non-dimensional radius R/R0 is important because as discussed earlier it contains insight into the onset of inertial cavitation (suggested by Leighton to be when

R/R0 = between 2 and 2.3 [35]). In the case that the inertial cavitation threshold pressure is 2, than the Morgan model predicts cavitation somewhere between 200 and 500 kPa (a thorough study of the cavitation predications of the Morgan equation are discussed in

Chapter 3). However, some groups have suggested that the onset of inertial cavitation

should be related to the kinetic energy of the bubble, and therefore the non-dimensional

wall velocity of the bubble (or Mach number, / ). Figure 4.4 displays the Mach number

푅̇ 푐 106 as a function of the same incident pressures as Figure 4.3. It is suggested by Vaughan that the inertial cavitation threshold is a Mach number of 1 [37]. In this case, the Morgan model predicts cavitation based on the Mach number between 500 kPa and 1 MPa.

Figure 4.4: Morgan model predictions of the Mach number. The predictions of microbubble non-

dimensional wall velocity are simulated using for the Morgan model at four pressure

amplitudes. The simulations have incident pressure amplitudes (top left to right) of 50, 200,

500, and 1000 kPa. The velocity change becomes non-linear with increasing incident

pressure, until the speed becomes spectrum-like, with very larger compression velocity

(negative velocity) compared to the expansion velocity.

Morgan adds two terms to the Herring equation to account for the effect of both the

1 and 12 elastic modulus and shell viscosity, which are: ( ), 2휒 푅0 2 3푅̇ 푅̇ 푅 � 푅 � � − 푐 � 휇푠ℎ휀 푅 푅−휀 107

respectively. Morgan’s third contribution to the equation is in the portion of the equation

that describes the pressure directly outside the bubble, assumed in the RPNNP as

displayed in Equation 1.16. However, Morgan adds that the pressure outside the bubble

should also be affected by the elastic modulus of the shell, such that:

2 3 2 = + + 3훾 1 1 0 ̇ ̇ 퐿 0 휎 ퟐ흌 푅 훾푅 휎 푅 푃 �푃 0 ퟎ� � � � − � − � − � 푅 푹 푅 푐 푅 푐 (Equation 4.2)

This is somewhat perplexing, as this is assuming that pressure drop is somehow related to

not only the Laplace pressure, but also the elastic modulus. The effect on the equation is

to aid acceleration of the bubble wall to return to zero when no ultrasound pressure is

being applied as it negates the 1 term when R = R0 and = 0 (no pressure 2휒 푅0 2 3푅̇ 푅 푅 푐 ̇ function). This is important to bear� in� mind� − as �it will be an important allusion푅 to the next

model examined, Philippe Marmottant’s modification (in the following section).

4.1.2.3 Marmottant Model

Philippe Marmottant developed his microbubble dynamic model is 2005, and is a further

improvement inspired by the Morgan model [36]. Marmottant’s model is again rooted in

both the Herring and RPNNP. In addition to the terms presented in the modified Herring equation (Equation 3.4), Marmottant adds the effect of dilatational viscosity of the shell,

which was originally introduced by Chatterjee in 2003 [83]. Marmottant’s original contribution, as alluded to in the previous section, was the effect dynamic surface tension 108

(σ(R)). Marmottant correctly states that the surface tension of a shelled microbubble

should not be constant, as it had previously been assumed to be, because surface tension

is a function of the bubble surface area (and therefore the radius). In Morgan’s model, the surface tension (in the Laplace pressure) is affected by the elastic modulus, χ, for all bubble radii. Marmottant argues that this cannot be correct because this would assume that the surface tension increase as the bubble expands (when in reality it should be the exact opposite) [36]. Marmottant therefore defines three regimes of shelled microbubble oscillation; a buckled state at small radii (based on the work of Mark Borden [84]), an

elastic state at intermediate radii, and a ruptured state at large radii. The thresholds of these regimes are loosely defined as Rbuckling = 0.99*R0, and Rruptured =

1/2 Rbuckling(1+σwater/χ) (with Relastic being anything in between). The dynamic surface

tension is therefore defined within these regimes as:

0 if R ≤ Rbuckling

σ χ 1 (R) = 2 if Rbuckling ≤ R ≤ Rbreak-up 푅 2 { σ�water푅푏푢푐푘푙푖푛푔 − � if R ≥ Rruptured (Equation 4.3)

Within these criteria, several scenarios arise. At very small pressure amplitudes

(therefore small oscillations), the microbubble can stay in the elastic region with stability.

In this case, the Morgan model would be correct (at least in terms of the addition of the

term mentioned in the previous section). For large pressure amplitudes, however, the

bubble should experience all of these regimes in a single oscillation. The surface tension 109

will therefore vary based on the instantaneous radius between 0 and 72 mN/m (σwater).

The Marmottant model is presented below in Equation 4.4:

3 1 2 ( ) 3 2 ( ) 4 4 + = + 1 2 3훾 2 휎 푅0 푅0 훾푅̇ 휎 푅 휇푅̇ 휅푠푅̇ 푅푅̈ 푅̇ ��푃0 � � � � − � − − − 2 − 푃0 휌 푅0 푅 푐 푅 푅 푅 ( )

− 푃 푡 � (Equation 4.4)

where κs is the dilatational viscosity. The form of Marmottant’s equation is very familiar

to those which have been presented throughout this work, with the exception of a few

new terms (here, the dilatational viscosity and dynamic surface tension). Since

Marmottant himself makes comparisons to the Morgan equation, it is interesting to

investigate their responses side by side. Figure 4.5 displays the microbubble response

(again in both non-dimensional radius and Mach number) of both the Marmottant

equation (red line) and the Morgan equation (black line). The simulations were created

-9 with the same Morgan model parameters as in Section 4.1.2.2, a κs of 7*10 N s/m, and

incident pressure amplitudes of 100 kPa (left panels) and 500 kPa (right panels). The

Marmottant model proves to be more stable both in the shape of the oscillations and the magnitude of the oscillations. Again, the difference in the two models is magnified at higher pressures. The Marmottant model is understandably more stable with the dynamic surface tension, when the radius is large, damping is also at its largest (σ(R) = σwater), and as the bubble contracts, damping is at its smallest (σ(R) = 0). 110

Figure 4.5: Marmottant and Morgan model predictions. The Morgan model (black line) and modified

Marmottant model (red line) simulations are compared. The simulations in the first column

have an incident pressure of 100 kPa, and the second column has an incident pressure of 500

kPa. The first row displays the response of the non-dimensional radius (R/R0) and the second

row displays the response of the non-dimensional wall velocity (or Mach number; ( / )).

푅̇ 푐

4.2 Colloidal Approach to Microbubble Dynamics

All the models aforementioned make the claim to be able to accurately predict microbubble oscillations. Many of the research groups responsible for deriving these models prove their accuracy by taking high speed images of an oscillating microbubble 111

under an ultrasound field [29, 36, 54, 55, 85]. Most of these models are typically very accurate under two conditions: the incident sound pressure is relatively low (<100 kPa), and certain material properties are allowed to vary as fitting parameters. These conditions allude to the weakness of some of these models; they break down at high incident pressures and they require fitting parameters (and are therefore not truly predictive). From a colloid science approach, another perceived weakness of these models is the use of bulk material properties, such as the shell stiffness parameter (Sp), elastic modulus (χ), and shell viscosity (µsh). Bulk material properties assume that the material in question is homogeneous throughout, whereas a microbubble is comprised of only a thin solid shell and larger encapsulated volume of gas. From this perspective, interfacial material properties are desired, such as the surface tension (σ) and the

dilatational viscosity (κs).

The influence of the shell should be described by a well defined surface material

property, not a bulk property. One such appropriate property is the area expansion

modulus, KA. The area expansion modulus can be interpreted as the first derivative of

surface tension with respect to area (or the second derivative of the Gibbs free energy

with respect to area) [58].

= 훿휎 퐾퐴 � � 훿퐴 푛푠 (Equation 4.5)

112

where ns is the number of surfactant molecules in the monolayer. To incorporate this

relevant membrane phenomenological parameter into a microbubble oscillation model,

KA must be recast in terms of a pressure drop it enacts on the interface. By definition, KA

is equal to the applied tension, τ, divided by the strain caused by the applied tension, αt:

= 휏 퐾퐴 훼푡 (Equation 4.6)

and αt is equal to the change in surface area (A) divided by the initial surface area (A0) of

the microbubble.

4 ( ) ( ) = = = 4 2 2 2 2 ∆퐴 휋 푅 − 푅0 푅 − 푅0 푡 2 2 훼 0 퐴 휋 푅0 푅0 (Equation 4.7)

Finally, the tension t is defined as:

1 = 2 휏 − ∆푃푅 (Equation 4.8)

Combining Equations 4.6, 4.7, and 4.8, KA has been rearranged as a function of pressure

drop and can be added to an RPNNP-like equation.

113

( ) = 2 2 2 퐾퐴 푅 − 푅0 ∆푃 − 2 푅푅0 (Equation 4.9)

With the KA term identified, the remainder of the model can be easily derived from the

energy balance, as demonstrated with Rayleigh’s equation in Chapter 1. This new

colloidal model also takes some insight from past modifications of Rayleigh’s equation.

Both Poritsky and Herring’s modifications are taken into account, along with Chatterjee’s

addition of the surface dilatational viscosity (but not Marmottant’s his dynamic surface tension, as discussed later in this chapter). This new colloidal model is presented below, in Equation 4.10:

3 1 2 3 2 4 2 ( 2 2) + = + 3훾 1 1 2 2 퐴 표 2 0 ̇ ̇ ̇ 퐾 푅 − 푅 0 휎 푅 훾푅 휎 푅 휇푅 푅푅̈ 푅̇ ��푃 � � � � − � − � − � − − 표 휌 푅0 푅 푐 푅 푐 푅 푅푅 4 ( ) 휅푠푅̇ − 2 − 푃0 − 푃 푡 � 푅 (Equation 4.10)

This equation represents a step forward in microbubble dynamics equations for two

reasons. First, it employs only relevant surface material properties, and no bulk material

properties. Second, it can potentially be used as a fully predictive model (with no fitting

parameters) by knowing only the KA of the microbubble being analyzed. The KA is extensively measured in the literature for lipid bilayers, but can be measured for unique 114

samples (like microbubbles or ultrasound contrast agents) by a pipette aspiration method

[86]. Predictions of microbubble cavitation behavior using KA will be discussed in the

following sections.

The colloidal model can be simulated in the same fashion as the aforementioned

microbubble oscillation models. The equation will be numerically solved using the same

-9 parameters as the previous models (P0 = 10130 Pa, R0 = 1 mm, σ = 51 mN/m, κs = 7*10

3 N s /m, KA = 0.05 N/m, γ = 1.07, c = 1540 m/s, ρ = 998 kg/m , and µ = 0.001 Pa s). P(t) has the form of Figure 1.13 (4 cycle sine burst), with amplitudes of 50, 200, 500, and

1000 kPa.

115

Figure 4.6: Colloidal model oscillation predictions. The predictions of microbubble non-dimensional

radius are simulated using for the colloidal model at four pressure amplitudes. The

simulations have incident pressure amplitudes (top left to right) or 50, 200, 500, and 1000

kPa. The oscillations are stable, but are already non-linear at 50 kPa.

The oscillations predicted by the colloidal model are very stable, even up to 1 MPa. The oscillations are slightly non-linear at 50 kPa (slightly larger peak positive pressure than peak negative pressure). At greater pressure amplitude, the oscillations take on a saw- tooth shape, and the oscillations exceed the cavitation threshold criteria of R/R0 = 2 between 200 and 500 kPa. In previous models, the radius is prone to increase on subsequent cycles. The colloidal model predicts a slightly lower magnitude of oscillations in comparison with the Marmottant model. Additionally, the Mach number can be simulated at the same incident ultrasound pressure with the colloidal model

(results presented in Figure 4.7). Similar to the other models presented in this chapter, the oscillations of the wall velocity become increasingly non-linear as the incident pressure increases, and become spikes at 1 MPa. The Vaughan cavitation criteria (where the Mach number exceeds 1) is also satisfied at 1 MPa with this model.

116

Figure 4.7: Colloidal model Mach number predictions. The predictions of microbubble non-

dimensional wall velocity are simulated using for the colloidal model at four pressure

amplitudes. The simulations have incident pressure amplitudes (top left to right) or 50, 200,

500, and 1000 kPa. The oscillations in velocity slowly become the characteristic spectrum-

like spikes at 1 MPa.

4.3 Simulating Cavitation with the Colloidal Model

As aforementioned, other studies compare their presented models for microbubble oscillations with high speed camera data acquired while a microbubble is oscillating under ultrasound. This technique is applicable when studying the dynamic radius of a single bubble. In this work, the accuracy of the proposed model will be evaluated using 117

the cavitation simulation technique described in Chapter 3. Comparing experimental

cavitation data with simulated cavitation profiles gives improved accuracy because it

allows for the analysis of the behavior of an entire population of microbubbles, not just a

single one. This is beneficial because typically commercial contrast agents display a

range of sizes in their microbubble populations, which is known to affect the oscillation

dynamics. With the cavitation comparison, a real world size distribution of microbubbles

can be evaluated.

4.3.1 Simulation Method

Reviewing what was described earlier in Chapter 3, the simulated cavitation thresholds

are simulated as follows. The colloidal model (Equation 4.10) will be numerically solved

by MATLAB (ode45, a non-stiff solver) for a series of initial radii, 0.1 – 5 µm. At each

R0, the solver iteratively increases the magnitude of P(t) until the given cavitation

criterion is met (for example, R/R0 = 2). At this point, the program records the lowest

value of the magnitude of P(t) that satisfies the cavitation criteria, and marks it as PT0.

The program then continues the R0 loop until it has identified a PT0 for every

corresponding R0. By this method, the program can generate a plot which describes the predicted incidence of inertial cavitation depending on the initial radius of a microbubble,

shown here in Figure 4.8 (for the given set of constant parameters listed in the figure

caption).

118

Figure 4.8: Prediction for the incidence of cavitation. The blue line represents the simulated lowest

value of PT0 which satisfies the criterion R/R0 = 2 for each of the radii examined. The

simulation was run with constant parameters: P0 = 10130 Pa, R0 = 1 mm, σ = 51 mN/m, κs =

-9 3 7*10 N s /m, KA = 0.05 N/m, γ = 1.07, c = 1540 m/s, ρ = 998 kg/m , and µ = 0.001 Pa s.

In Figure 4.8 an initial radius of 0.8 µm is shown to be the radius which requires the lowest pressure to inertially cavitate. Relatively lower and higher radii require increasingly more pressure to reach the cavitation threshold. To then build the cavitation destruction profile, the program overlays the above figure with the measured size distribution of the given sample, shown below in Figure 4.9 from the 95 mole% DSPC, 5 mole% DSPE-PEG 3000 composition. 119

Figure 4.9: Comparison of measured size distribution with “destruction distribution”. Figure 4.8 is

overlaid with the measured size distribution for the 95 mole% DSPC, 5 mole% DSPE-PEG

3000 composition (green line). At a given pressure, the fraction of size distribution under the

blue curve is predicted to be cavitated.

To build the cavitation destruction profiles, Figure 4.9 is analyzed for its overlapping regions at all pressures. At low pressures below the blue line, no cavitation is predicted because at this pressure none of the measured sizes are ideal for cavitation. At pressures above the blue line, some weighted fraction of the size distribution is predicted to be cavitated, because that initial size will produce oscillations greater than the threshold criterion. At very high pressures (greater than 2.5 MPa), almost 100% of the measured size distribution is beneath the cavitation criteria line (blue) and is predicted to be cavitated. The destruction profiles presented below are generated simply by equating the 120

weighted percentage of the size distribution under the blue curve to the percent of

microbubbles destroyed.

4.3.2 Cavitation Profile Sensitivity

By changing the relevant surface material parameters, it is anticipated that any of the

measured cavitation profiles can be fit with a simulated profile. Altering the surface

properties is logical as these would be the only parameters affected by a change in

monolayer composition. Those relevant parameters are the area expansion modulus (KA),

the surface tension (σ), and the dilatational viscosity (κs). Of course, building the

minimum cavitation criteria curve (blue line in the figures above) is dependent on the

selected inertial cavitation criterion. First, cavitation profiles are built with the above

method for inertial cavitation threshold criteria of R/R0 = 2, 3, 4, 6, and 8 (Figure 4.10, below). This may seem excessive to classical cavitation theorists, as Leighton had described the threshold value to be somewhere between 2 and 2.3 [35]. However recently, O’Brien has used threshold values between 3.4 and 8 to describe the cavitation behavior of Definity [53].

Figure 4.10 displays the sensitivity of the simulated cavitation profiles to changes in the threshold criteria. This aids in the identification of the proper value for predicting cavitation profiles. The shape of the cavitation profile remains fairly constant between the different cavitation criteria, however to onset of cavitation varies greatly between 0.4 and 2.1 MPa for the range analyzed. All other parameters except the threshold criteria are held constant. 121

Figure 4.10: Predicted sensitivity to cavitation threshold. The simulated cavitation profiles are

modeled for cavitation threshold criteria of R/R0 = 2, 3, 4, 6, and 8. The relevant

-9 phenomenological constants are: σ = 51 mN/m, κs = 7*10 N s /m, and KA = 50 mN/m. As

the threshold criterion increases, the shape of the curve appears constant and the pressure

incidence of cavitation is increased.

In addition to altering the threshold, the surface material parameters from the colloidal model will also be varied in a physically significant way to determine the cavitation profiles sensitivities to them. Figures 4.11 – 4.13 display the sensitivity of the cavitation profiles to changes in KA, κs, and σ, respectively. The parameter values studied are: KA =

5, 10, 25, 50, and 100 mN/m, κs = 3, 4, 5, 6, 7 nN s/m, and σ = 5, 10, 25, 50, 72 mN/m.

122

Figure 4.11: Predicted sensitivity to area expansion modulus. The simulated cavitation profiles are

modeled for area expansion moduli of KA = 5, 10, 25, 50, and 100 mN/m. The cavitation

threshold criterion is R/R0 = 4, and the relevant phenomenological constants are: σ = 51

-9 mN/m, and κs = 7*10 N s /m. As the area expansion modulus increases, the growth rate of

the curve becomes less steep and the pressure incidence of cavitation is increased.

123

Figure 4.12: Predicted sensitivity to dilatational viscosity. The simulated cavitation profiles are

-9 modeled for dilatational viscosities of κs = 3, 4, 5, 6, and 7 *10 N s/m. The cavitation

threshold criterion is R/R0 = 4, and the relevant phenomenological constants are: σ = 51

mN/m, and KA = 50 mN/m. As the dilatational viscosity increases, the growth rate of the

curve decreases slightly and the pressure incidence of cavitation is increased slightly.

124

Figure 4.13: Predicted sensitivity to surface tension. The simulated cavitation profiles are modeled

for surface tension of σ = 5, 10, 25, 50, and 72 mN/m. The cavitation threshold criterion is

-9 R/R0 = 4, and the relevant phenomenological constants are: κs = 7*10 N s /m, and KA = 50

mN/m. As the surface tension increases, neither the growth rate of the curve or the

incidence of cavitation is affected.

Of these three surface material properties, variations in KA have the greatest effect on the cavitation profiles. Increasing KA both decreases the growth rate of the destruction profile and increases the cavitation threshold pressure significantly. Variations in κs influence the shape and threshold pressure in the same way, but to a lesser extent within the physically relevant range. The surface tension is a well defined parameter for many interfaces, and is worth further discussion. The value for an air/water interface is 72 mN/m, and the addition of surfactants (such as the lipid shell) effectively decreases the 125

value of the surface tension. Values for the surface tension of microbubbles have been

estimated by previous researchers to be in the range investigated in Figure 4.13 [54, 87,

88]. As discussed earlier in this chapter, Marmottant argues that the surface tension is

variable between 0 -72 mN/m depending on the oscillation status of the microbubble.

However, as shown through the simulation in Figure 4.13, values of the surface tension in this range make a very minimal difference in both the growth rate and cavitation threshold pressure in the destruction curves. This serves as good justification for using a

constant value for surface tension in the colloidal model.

4.4 Predictive Model for Microbubble Cavitation

Armed with the sensitivities for the variables which theoretically could be affected by a

change in membrane composition, the colloidal model can be utilized for predicting the

cavitation profile of microbubbles with compositional changes. However, it is necessary

to understand which of the variables studied above will change and by how much as a

function of the compositional change.

As described earlier, as PEG functionalization increases from 1 – 10 mole%, the

interactions between PEG molecules changes from a regime where they do not interact

(mushroom) to one in which they are close enough together to interact (brush). Lin and

Thomas report that for PEG 2000, this transition should occur at around 4 mole% PEG,

and that the membrane should be saturated with PEG molecules at 8 mole% [26]. 126

Although this is a function of PEG molecular weight, we can use these as general guidelines. For example, the 1 and 2.5 mole% samples are firmly in the mushroom regime, while the 10 mole% samples are firmly in the brush (5 and 7.5 mole% being somewhere in the transition closer to brush). This regime change brought on by increasing membrane surface functionalization of PEG can be described by a change in on the area expansion modulus, KA [62, 89, 90]. KA is a known function of the PEG composition, molecular weight, and interaction regime. In the mushroom regime, the value of KA is insensitive to changes in molecular weight and compositional change, which can be seen in Figure 4.14, where all the measured cavitation profiles for mushroom regime compositions are plotted together (1 and 2 mole% PEG for all molecular weights).

127

Figure 4.14: Mushroom regime cavitation profiles. The measured cavitation profiles for all

mushroom regime shell compositions are plotted together (1 and 2.5 mole% PEG, all

MWs). All the curves overlap fairly well and have similar values for PT0, PT50, and PT100.

All the cavitation profiles measured from shell compositions in the mushroom regime

overlap, with both the same shape and inertial cavitation threshold. This result can be

taken that all the shell compositions in this regime have the same material parameters,

specifically KA, which supports the earlier hypothesis. KA0 will be considered as the

mushroom regime value of KA, and will be determined with a fitting routine using the measured data. The value of KA0 is found to be 25 mN/m, as determined by fitting curves

to the measured data for the 99 mole% DSPC, 1 mole% DSPE-PEG 2000 shell

composition, illustrated in Figure 4.15.

128

Figure 4.15: Mushroom regime fitted cavitation profile. A simulated cavitation profile is compared to

a mushroom regime measured cavitation profile (99 mole% DSPC, 1 mole% DSPE-PEG

2000). The simulation was generated with a cavitation threshold criterion is R/R0 = 3, and

-9 phenomenological parameters of: σ = 51 mN/m, κs = 7*10 N s /m, and KA = 25 mN/m. In

general, the colloidal model gives good agreement to the experimental data.

This simulated profile, built using colloidal model with threshold criterion R/R0 = 3, σ =

-9 51 mN/m, κs = 7*10 N s /m, and KA0 = 25 mN/m, gives good agreement to the experimental data. Since it is desired to design a predictive model, the value of KA must

now be calculated for changes in shell composition, and then compared to other measured

profiles. KA in the transition or brush regime is not constant, and is a function of both the

PEG molecular weight and mole fraction, given by Equation 4.11:

+ ln ( ) = 8 5 �∆ 푋0 � 퐾퐴 퐾퐴0 3 5 푁 (Equation 4.11)

where ∆ is the adsorption energy (normalized by kT), X0 is the mole fraction of

PEGylated lipids in the shell, and N is the number of PEG repeat units in a PEG

molecule. N can simply be determined by dividing the total MW of the PEG by the MW

of a single PEG repeat unit (44 g/mole). The adsorption energy is somewhat more

nebulous for these changes in shell composition, but will be held constant for the

purposes of this work. If the adsorption energy is set to 8.5 kT, then the predicted values 129

of KA for the studied set of PEG MW and mole fraction can be described by Figure 4.16,

below.

Figure 4.16: Predicted KA for various shell compositions. This figure displays the predicted values of

KA using Equation 4.11 for shell compositions of 1 – 15 mole% DSPE-PEG, molecular

weights 1000 – 5000 g/mole. The adsorption energy is assumed to be 8.5 kT. Mushroom

regime compositions display KA = KA0 = 25 mN/m, and brush regime compositions exhibit

an increase in KA with both increasing PEG composition and decreasing PEG MW.

It can be observed from the figure that KA is unchanged for mushroom regime shell

compositions, but varies as a function of both X0 and N for brush regime compositions.

In fact, KA increases with increasing PEG composition in the monolayer, but decreases

with increasing PEG molecular weight. While this may seem counter-intuitive, recall the 130

results of the measured inertial cavitation threshold pressures from Chapter 3. In those

experiments, the PT50 (peak negative pressure to destroyed 50% of a microbubble

population) increased with PEG composition, but decreased with PEG molecular weight,

a result which lends credence to the theory.

For the combination of the colloidal model and the KA relation (Equations 4.10 and 4.11)

to be truly predictive, experimental destruction curves from the brush regime should be

able to be forecast by these equations. The fitted curve to determine KA0 fits all the

destruction profiles from the brush regime (see Figure 4.14). A predicted curve for the measured cavitation data from the 90 mole% DSPC, 10 mole% DSPE-PEG 2000 is therefore created using the same variables as for the mushroom regime prediction, with the exception of a new predicted KA, determined by Equation 4.11 to be 70 mN/m. The

resulting predicted line is overlaid on the measured cavitation data for that shell

composition in Figure 4.17. The prediction (green line) provides very good agreement

with the data, proving that the colloidal model can be used as a predictive model for

small changes in shell composition.

131

Figure 4.17: Brush regime predicted cavitation profile. A predicted cavitation profile is compared to

a brush regime measured cavitation profile (90 mole% DSPC, 10 mole% DSPE-PEG 2000).

The simulations was generated with a cavitation threshold criterion is R/R0 = 3, and

-9 phenomenological parameters of: σ = 51 mN/m, κs = 7*10 N s /m, and KA = 70 mN/m.

The colloidal model is able to give good agreement to the experimental data by only

altering the KA value from the mushroom regime determined KA0 and calculated from

Equation 4.11.

The use of a predictive model for determining the inertial cavitation threshold of ultrasound contrast agents is of obvious importance. In this way (or by measuring the KA of the shell material) the onset of the negative bioeffects associated with inertial cavitation can be avoided. Additionally, the full extent of cavitation can also be predicted 132 for drug delivery applications, and bubbles can be tailor made - by tuning their shell composition - to achieve either (or both) of these ends.

4.5 Conclusion

The focus of this chapter has been to highlight the importance and accuracy of microbubble dynamics equations. Classic equations, namely the RPNNP and Herring equation, are analyzed along with three (of many) equations that account for the addition of a microbubble shell. A new model was therefore developed based on the advancements put forth the RPNNP, Herring, and Marmottant equation, with the addition of the effect of the area expansion of the bubble. The use of a rigorous surface property like the area expansion modulus allows the developed colloidal model to explain the cavitation profiles measured in Chapter 3. Additionally, with the aid of an equation that describes the area expansion modulus as a function of shell composition, the colloidal model predicates its power in predicting the cavitation profiles of brush regime shell compositions. 133

CHAPTER 5: Resonance Frequency of Microbubbles

5.1 Introduction to Resonance Frequency

Due to their functionality as ultrasound contrast agents and drug delivery vehicles,

shelled microbubbles have garnered significant interest over the past 20 years [9, 28, 91].

Microbubbles which are effective in contrast and drug delivery modalities are typically

characterized by a thin shell – often a monolayer – which coats and stabilizes a gas core.

For ultrasound contrast applications, microbubbles rely on their ability to reflect and

backscatter sound waves which can be detected and interpreted by a clinical ultrasound

imager. For this reason, microbubble stability is of importance to commercial

manufacturers. The most recent formulations of microbubbles are between 1 – 10 µm in

diameter and consist of a polymer, phospholipid, or protein shell, which encapsulates a

fluorinated heavy gas [1, 12, 92]. These microbubbles are often further stabilized by the

addition of a covalently linked polymer, such as polyethylene glycol (PEG), to prevent

coalescence and uptake in vivo by steric hindrance [25, 61, 74].

Another phenomenon which influences microbubble stability is that of cavitation.

Microbubbles in a sound field respond to the positive and negative pressure components of wave by oscillations [93]. The oscillation period is determined by the driving frequency of the ultrasound, while the magnitude of the oscillations is mainly driven by the amplitude of the sound pressure. At relatively low pressures, below the so-called 134

cavitation threshold, microbubbles will exhibit sustained oscillations (also called stable

cavitation). However, above this threshold – which is accepted to be when the

microbubble’s wall velocity exceeds the speed of sound in the media – the microbubble

undergoes a violent collapse and implosion, termed inertial cavitation [66, 87]. Inertial

cavitation is the unwanted outcome for a clinician (and patient) for two reasons, one

being the destruction or fragmentation of the contrast agents themselves, and another

being the potential for the subsequent shockwave to damage nearby cells [40, 94]. In

previous chapters, it was demonstrated that the inertial cavitation threshold depends on microbubble shell composition, namely the mole fraction and molecular weight of functionalized PEG. However, given that the magnitude of microbubble oscillations is a function of the microbubble resonance frequency, it is hypothesized that shell composition driven changes in inertial cavitation threshold stem from shell composition

driven changes in resonance frequency. Whereas many previous studies [9, 28, 91] have

focused mainly on the dynamics of commercially available contrast agents, it is of

interest to test the hypothesis by investigating the resonance frequency dynamics with

controlled variations in shell composition, both experimentally and with a well defined

microbubble dynamics equation.

5.2 Detection of Microbubble Resonance Frequency

5.2.1 Materials 135

The phospholipid 1,2-Distearoyl-sn-glycero-3-Phosphocholine (DSPC) and Polyethylene

Glycol (PEG) functionalized lipid 1,2-Disteroyl-sn-Glycero-3-Phosphoethanolamine-N-

[Methoxy(Polyethyleneglycol)-1000], ammonium salt (DSPE PEG 1000) were purchased from Avanti Polar Lipids (Alabaster, AL). The 2000, 3000 and 5000 g/mol molecular weight DSPE PEG functionalized lipids were also supplied by the above. Sulfur

Hexafluoride (SF6) was purchased from Airgas (Allentown, PA). All other reagents used were of analytical grade.

5.2.2 Microbubble Preparation

As described earlier and in previous works [52, 95], a lipid film containing various

mole% of DSPC and a PEG functionalized lipid is deposited onto a 20 ml scintillation

vial from stock solutions dissolved in chloroform by N2 spin drying followed by 2 hours

in vacuum. The dried film is then rehydrated with 5 ml of aqueous phosphate buffered

saline (PBS) solution (pH 7.4) by sonicating the sample (Hielscher UP200S Ultrasonic

Processor, Hielscher Ultrasonics, Teltow, Germany) for approximately 3 minutes at 20%

amplitude. This has the dual effect of dissolving the lipid mixture in solution and raising

the temperature above that of the DSPC gel phase transition temperature, 55 oC. The

rehydrated solution is then cooled and aliquoted out into 2 ml serum vials and sealed.

The head space air is then evacuated from the vial and replaced with the fluorinated

heavy gas, SF6. Finally the vials are vigorously shaken using the Vialmix shaker

(Lantheus Medical Imaging, North Billerica, MA) in order to disperse the gas phase. The resultant microbubbles are allowed to settle at room temperature for 30 minutes; long term storage should occur at 2-8 oC. These techniques successfully produce stable 136 microbubbles with a 1-2 µm diameter. As mentioned in previous sections, the size distribution of the population of microbubbles was determined by a MATLAB

(Mathworks, Natick, MA) image segmentation program. Samples of the selected shell compositions are separately prepared by the same method listed above and diluted to aid the analysis of the program, since overlapping or clustered microbubbles cause anomalous results. The program then detects circles imaged by an optical Carl Zeiss

Axioskop 2+ microscope (Carl Zeiss AM, Oberkochen, Germany) and reports the diameter distribution of the sample.

5.2.3 Resonance Frequency Measurement

The resonance frequency detection setup, shown in Figure 5.1, consists of two 7.5 MHz center frequency, 5 cm spherical focus ultrasound transducers (Olympus NDT, Waltham

MA) positioned axially 10 cm apart with their overlapping foci inside a cylindrical steel sample chamber, filled with PBS, and sealed with rubber gaskets. The transmitter is driven by an Inoson model MT 06013 pulser/receiver (Inoson, St. Ingbert, Germany), and the received signal is filtered between 1 KHz and 36 MHz and amplified by +26 dB by a

Panametrics model 5900RR (Olympus NDT, Waltham MA), and finally digitized by an oscilloscope (GaGe Compuscope, Lockport IL).

137

Figure 5.1: Resonance frequency detection setup. The resonance frequency of lipid shelled

microbubbles was determined by a system consisting of two 7.5 MHz center frequency

spherically focused (5 cm) ultrasound transducers positioned axially 10 cm apart inside a steel

cylinder, such that their foci overlap. The transmitter is driven by an Inoson pulser/receiver,

which emits a chirp that is attenuated inside the sample chamber by the contrast agents (and

minimally by the PBS). The received signal is amplified by +26 dB and band pass filtered

between 1 kHz and 36 MHz, then finally digitized by a GaGe oscilloscope. The data is saved

and processed by MATLAB.

The transmitted signal is defined by a chirp function, increasing in frequency from 750 kHz to 13 MHz over a period of 25 µs (shown in Figure 5.2 A, B) with a pulse repetition time of 1 ms for a total of 100 pulses. This pulse train undergoes 40 repetitions with one second pauses to analyze the change in frequency response over time. The peak negative pressure of the ultrasound was limited to below 10 kPa to ensure that the microbubbles were not being destroyed during sonication and to limit nonlinear oscillations emanating from the microbubbles. 138

Figure 5.2: Acoustic views of the chirp. A The received signal waveform of a chirp emitted at 10 kPa

with a dynamic frequency beginning at 0.75 MHz and ending at 13 MHz. The chirp signal

was selected because it covers a broad spectrum of frequencies in a relatively small time

period (25 µs). This ensures that microbubbles are not destroyed, and that a full frequency 139

response can be recorded from a population of bubbles. B An acoustic spectrogram of

received signal. Here the increase in frequency within the 25 ms is easily visible. Harmonics

are also visible at higher power than the noise. Both figures were acquired from the reference

signal (PBS only).

The signal travels axially through the sample chamber and interacts with the contrast

agent population floating freely within the sample chamber at a concentration of approximately 15000 microbubbles per ml. The microbubbles are prepared as described earlier and consist of a set of compositions encompassing PEG molecular weights of

1000 – 5000 g/mol and PEGylated lipid shell composition of 1 – 15 mole%

(compositions which match earlier cavitation studies). The received signal is attenuated by the microbubbles depending on their concentration and resonance frequency at each frequency of the chirp. The received signal is then processed by MATLAB to determine the attenuation amplitude in the frequency domain to determine which frequency yields the highest attenuation for a given sample. The frequency spectra are normalized by a reference spectrum, generated with signals traveling through only PBS.

5.3 Reference Spectrum and Concentration Calibration

By this technique, spectra from samples of microbubbles of varying composition, concentration, or size can be analyzed. First, a reference spectrum of the sample chamber devoid of microbubbles must be produced to ensure a good signal, and to compare results when a population of contrast agents is present inside the chamber. As seen in Figure 140

5.3, the 7.5 MHz transducer is sufficiently broadband to generate a spectrum that has a -

20 dB bandwidth of approximately 12 MHz, ranging from 300 kHz to 12 MHz. The

noise floor is reached at 25 MHz at -65 dB, which will yield a high signal to noise ratio

within the -20 dB bandwidth. Therefore the recorded data will only be analyzed within

the -20 dB bandwidth. The chirp in Figure 5.2 A, B is also generated from this reference measurement.

Figure 5.3: Reference acoustic spectrum. A spectrum is obtained while the sample chamber is devoid

of microbubbles and contains only PBS. The spectrum shows that the signal has a -20 dB

bandwidth of approximately 12 MHz, ranging from 300 kHz to 12 MHz. The noise floor is

reached at 25 MHz, at -65 dB, which will yield a high signal to noise ratio within the -20 dB

bandwidth. Therefore the recorded data will only be analyzed within the -20 dB bandwidth.

Now, any differences in the reference spectrum and the subsequent measured spectrum

can be attributed to the addition of a sample into the control volume (holding all other 141 variables constant). The resulting transmission minimum in these new normalized spectra is the resonance frequency of the sample. However, there are several factors which influence shape of the received spectrum, but not necessarily the resonance frequency. First, the size polydispersity is once again relevant. The more monodisperse the population of microbubbles, the sharper the transmission minimum will be. This is logical because the absolute minimum of total attenuation should be the resonance frequency of the highest point of the size histogram, and the breadth of the size distribution relates to the breadth of the transmission minimum. Secondly, the concentration of the microbubbles which attenuate the transmitted sound also affect the shape of the curve. As seen in Figure 5.4, increasing the concentration of microbubbles increases the magnitude of total attenuation, most evident around the resonance frequency. Figure 5.4 shows a single composition of microbubbles (92.5 mole% DPSC,

7.5 mole% DSPE-PEG5000), being successively diluted from the experimental concentration – roughly 15000 microbubble per ml – to a concentration of about 1500 microbubbles per ml, at which point the transmission minimum is difficult to resolve.

142

Figure 5.4: Effect of microbubble concentration on resonance frequency. The concentration of a

sample of 92.5 mole% DSPC, 7.5 mole% DSPE-PEG 5000 microbubbles was altered within

the sample chamber. From top to bottom the microbubble concentration is 1500, 3000, 5000,

7500, and 15000 microbubbles/ml. While the magnitude of the total attenuation varies from -

2 to -30 dB over this concentration range, the frequency of the minima is consistently near 2

MHz. Dotted lines represent the raw data, and solid lines are a moving average.

The raw acoustic data is represented by the dotted lines, where the smooth, solid curve

was produced from an adjusted moving average of the raw data. The moving average is

preferable for peak determination because raw acoustic data can exhibit chaotic spikes

which can skew the resonance frequency minimum, as seen above.

It is evident from Figure 5.4 that within an optimum concentration window, determined here to be between 1500 – 30,000 microbubbles per ml, the developed technique gives reliable results for the transmission minimum, or resonance frequency, for a single 143

sample. For the sample displayed the resonance frequency is approximately 2 MHz.

Below 1500 microbubbles/ml, there is not sufficient attenuation by the microbubbles to

sufficiently resolve a transmission minimum, and above 30,000 microbubbles/ml the microbubble field will attenuate almost all the transmitted ultrasound and the result will simply be the inverse of the reference spectrum. This also serves to justify the experimental concentration of 15000 microbubbles/ml, shown in Figure 4.A as the

bottommost line.

5.4 Resonance Frequency as a Function of Shell Composition

The resonance frequencies of the set of microbubble shell compositions are determined

by the technique described in Section 5.2 above. The attenuation of the set of

microbubbles shell compositions is then measured by recording the response of the chirp

when travelling through the population of microbubbles. An example of these response

results is shown in Figure 5.5. Here, the received signal of a population of microbubbles

consisting of 95 mole% DSPC and 5 mole% DSPE-PEG5000 is compared to a reference

(from Figure 5.3), and analyzed for its mean attenuation maximum.

144

Figure 5.5: Microbubble frequency dependent attenuation. The received signal is analyzed for its

attenuation, compared to a reference (as in Figure 5.3), for a population of microbubbles

consisting of 95 mole% DSPC and 5 mole% DSPE-PEG5000. Here, the raw data is

represented by the dotted lines, where the smoothed line is a moving average of the raw data.

The moving average is preferable for peak determination because raw acoustic data can have

chaotic spikes which skew the resonance frequency. For this population, the resonance

frequency is determined by mean maximum of the moving average, and has a value of 2.95

MHz. The experiment is shown here in triplicate to demonstrate the reproducibility of the

determined resonance frequency as well as the degree of signal attenuation.

For this population, the resonance frequency is determined by mean maximum of the moving average, and has a value of 2.95 MHz. The experiment is shown in triplicate to demonstrate the reproducibility of the determined resonance frequency (standard deviation of 112 kHz) as well as the degree of signal attenuation at the maximum (17.6 dB mean maximum, 0.7 dB standard deviation).

145

9000000

8000000

7000000 PEG Molecular 6000000 Weight [g/mol] 5000000 1000 2000 4000000 3000 Frequency (Hz) Frequency 3000000 5000

2000000

1000000

0 0 2 4 6 8 10 12 14 16 PEG Composition (%mol)

Figure 5.6: Measured microbubble resonance frequency as a function of shell composition. The

mean resonance frequency and standard deviation is shown for the complete set of

microbubble shell compositions ranging from 1 – 15 mole% DSPE-PEG, and PEG molecular

weights of 1000, 2000, 3000, and 5000 g/mol. In general, the resonance frequency of the

microbubble populations decreases with increasing molecular weight and also decreases with

increasing PEG composition. The four different molecular weights are the most similar at

low PEG compositions, but vary afterwards, with the exception of PEG 3000 and 5000. PEG

2000-5000 exhibit an asymptotic decrease with increasing PEG composition, with the

exception of a spike increase at 7.5 mole%.

This approach is then repeated for the entire set of microbubble shell compositions.

Figure 5.6 shows the mean resonance frequency and standard deviation for the complete set of microbubble shell compositions ranging from 1 – 15 mole% DSPE-PEG, and PEG molecular weights of 1000, 2000, 3000, and 5000 g/mol. In general, the resonance 146

frequency of the microbubble populations decreases with increasing molecular weight

and also decreases with increasing PEG composition. The four different molecular

weights are the most similar at low PEG compositions but vary afterwards, with the

exception of PEG 3000 and 5000. Samples of PEG 2000-5000 exhibit an asymptotic

decrease with increasing PEG composition, with the exception of a spike increase at 7.5

mole% (present in all MWs except PEG 5000).

5.5 Simulating Resonance Frequency

To describe a dynamic microbubble system as a function of shell properties, a

modification to the RPNNP equation is employed. In previous works, authors such as

Church and de Jong have proposed models which include the effects of the shell into

bubble dynamic equations [28, 91]. For the purposes of this study, an equation which

takes into account well defined shell material properties is desired, and therefore a

modification of Church’s equation, made by Lars Hoff, is employed [9]. The equation is

of specific interest because it incorporates the shear modulus (GS) and shell viscosity (µS) into an equation that solves for the attenuation of a signal by microbubbles as a function of frequency and size distribution. Hoff’s equation describing ultrasound attenuation in the presence of microbubbles is described below [9],

( , ) = ( , ) ( ) (Equation 4.1) ∞

훼 푎푒 휔 ∫0 휎푒 푎푒 휔 푛 푎푒 푑푎푒 147

where α is total attenuation, ω is frequency, ae is the size distribution, the integral of n(ae)dae is the area under the size distribution, and σe is the extinction cross section, given by:

( , ) = 4 , = (Equation ( ) 2 2 푐 훿 Ω 휔 2 2 2 2 휎푒 푎푒 휔 휋푎푒 푎푒휔0 1−Ω +Ω 훿 Ω 휔0 4.2)

where c is the speed of sound in the media, and the damping constant δ is defined as:

= 푑푆푒 (Equation 4.3) 퐿 푆 4휇 +12휇 푎푒 2 훿 휌퐿푎푒휔0

where µL is the media viscosity, ρL is the media density, dSe is the shell thickness, µS is the shell viscosity, and ω0 is described by:

= (3 + 12 ) (Equation 4.4) 1 1 푑푆푒 휔0 푎푒 �휌퐿 휅푝0 퐺푆 푎푒

where κ is the polytropic coefficient, p0 is the hydrostatic pressure, and GS is the shear modulus. For this set of equations, p0, ρL, µL, κ, c, and dSe are fixed by experimental conditions for a system of known shell material, encapsulated gas, and surrounding media

(values of which displayed in Table 5.1). The goal of the model will be to find good agreement to experimentally determined resonance frequency data by varying only the 148

shell material parameters, GS and µS. Details of the comparison follow in the materials/methods section.

Equation 4.1 was solved for the total attenuation by varying the frequency between 0.5 –

15 MHz (to match the size of the chirp) and with experimental size distributions, measured in a previous work for each composition [52]. Shear modulus and shell viscosity are varied within a physically relevant range, and the remaining parameters are held constant, the values of which are shown in Table 5.1.

Table 5.1: Hoff equation model parameters.

Hydrostatic pressure p0 10130 Pa

-3 Media density ρL 998 kg m

Polytropic exponent κ 1.07

Speed of sound in media c 1500 m s-1

Media viscosity µL 0.001 Pa s

Shell thickness dSe 3 nm

By analyzing the solution for the frequency that produces the maximum value of attenuation (within the relevant range of the chirp) the resonance frequency can be determined for each set of input parameters (GS and µS). Alternatively, this can be viewed as determining where the extinction cross section is a maximum. However, there is more than one set of inputs which give a specific resonance frequency solution. 149

Because of this, it is necessary to find an entire surface of solutions within the physically relevant range of input parameters; from these surfaces a best fit solution can be identified.

In order to describe this system as a function of material parameters of the shell, the Lars

Hoff model mentioned earlier is employed. By solving this equation for the frequency which produces the maximum value of attenuation (within the relevant range of the chirp), taken from the solution to Equation 5.1, a resonance frequency can be determined for each set of the selected input parameters (GS and µS). However, there is more than one set of inputs which give a specific resonance frequency solution. Because of this, an entire surface of solutions is investigated within the physically relevant range of input parameters. Theoretical resonance frequencies can be thusly determined for a range of input parameters – specifically, 0 – 2 Pa s in shell viscosity and 0 – 100 MPa in shear modulus. The plane of solutions for the theoretical resonance frequencies is displayed in

Figure 5.7.

150

Figure 5.7: Theoretical resonance frequencies. The Hoff model predictions of resonance frequency are

displayed as a function of both possible input parameters, namely shell viscosity and shear

modulus. General trends show that the increasing the shear modulus increases the expected

resonance frequency, while increasing the shell viscosity decreases the resonance frequency

slightly.

To evaluate the accuracy of the Hoff model on the experimental results, the solution plane in Figure 5.7 should be compared to the measured resonance frequency for each shell composition. A simple comparison involves taking the difference between the theoretical solutions and a given measured value, and finding the values of the input parameters which minimize the difference. This approach is demonstrated in Figure 5.8, below, for microbubbles with a 95% DSPC, 5% DSPE-PEG 2000 shell.

151

Figure 5.8: Finding best fits of resonance frequency. The difference between the modeled resonance

frequency and the measured resonance frequency for a microbubble population consisting of

95% DSPC and 5% DSPE-PEG2000 is plotted on the surface of the parameters used to

generate the modeled resonance frequencies- namely shear modulus (GS) and shell viscosity

(µS). Ranges for the two parameters are 0 – 2 Pa s in shell viscosity and 0 - 100 MPa in shear

modulus. To determine the best fit parameters, the zero crossing of the difference between

model and measured can be obtained. The zero crossing result, represented by the heavy

black line, is a set of best fit parameters.

Figure 5.8 shows the difference between the modeled resonance frequencies and the measured resonance frequency for a microbubble population consisting of 95% DSPC and 5% DSPE-PEG2000. The error difference is plotted on the surface of the parameters used to generate the modeled resonance frequencies- namely shear modulus (GS) and shell viscosity (µS). Again, ranges for the two parameters are 0 – 2 Pa s in shell viscosity 152 and 0 to 100 MPa in shear modulus. To determine the best fit set of parameters, the zero crossing of the difference between model and measured can be obtained (line where the modeled frequency is closest to the measured frequency). These best fit parameter lines can be determined for the entire set of shell compositions.

60000000

1% 50000000 2.5% 7.5% 40000000 5% 10% 30000000

12.5% 20000000 Shear Modulus Modulus (Pa) Shear 15% 10000000

0 0 0.5 1 1.5 2 Shell Viscosity (Pa s)

Figure 5.9: Modeled solutions for a set of contrast agents. The lines of zero crossing- or so called best

fit parameters - from the DSPC/DSPE-PEG2000 set, PEG compositions 1 – 15 mole%,

acquired similarly to that in Figure 5.8 are displayed. Interpolating between the lines of

measurement (at the different PEG compositions), a plane of possible solutions to shear

modulus and shell viscosity parameters can be drawn. The best fit lines decrease in both

slope and GS intercept (on the µS v GS plane) as the PEG composition increases, again with

the exception of 7.5 mole% PEG (x).

153

The lines of zero crossing constitute best fit parameters, which are displayed in Figure 5.9

from the DSPC/DSPE-PEG2000 set, with PEG compositions of 1 – 15 mole%. Between

the best fit lines (at the different PEG compositions), a plane of possible solutions to

shear modulus and shell viscosity parameters can be drawn. The best fit lines decrease in

both slope and GS intercept as the PEG composition increases, again with the exception

of 7.5 mole% PEG (x), a phenomenon which has propagated from the measured values.

5.6 Dependence of Cavitation Threshold on Resonance Frequency

One interesting comparison is to relate these resonance frequency results with previously determined inertial cavitation threshold pressure results for the same set of compositions

[52]. Recall Figure 3.10A, which displays the measured destruction profiles for a set of

contrast agents consisting of DSPC and DSPE-PEG2000 functionalized lipid, with compositions ranging from 1 – 10 mole% (data represented by: 1 mole% [x], 2.5 mole%

[o], 5 mole% [□], 7.5 mole% [∆], and 10 mole% [◊]). No cavitation is observed at PNP

less than 0.3 MPa for any composition, and the microbubble populations are not all

completely cavitated by the upper limit of pressure output from the pulser. PT50 is defined as the pressure required to destroy 50 percent of the microbubble population, for these samples ranging from 0.85 MPa and 1.2 MPa. For these compositions, PT50

increases with increasing PEG composition. By this same method, the mean cavitation

threshold was determined for the same set of compositions examined in the resonance

frequency study. 154

1.4

1.3

1.2

1.1 PEG Molecular 1 Weight [g/mol] 0.9 1000 2000 0.8 3000 5000 0.7 Cavitation Cavitation Threshold (MPa)

0.6

0.5

0.4 0 2000000 4000000 6000000 8000000 Resonance Frequency (Hz)

Figure 5.10: Experimental cavitation threshold and resonance frequency comparison. The

previously measures inertial cavitation threshold (PT50) of set of microbubble shell

compositions ranging from 1 – 15 mole% DSPE-PEG, and PEG molecular weights of 1000,

2000, 3000, and 5000 is plotted against the experimental results from the resonance

frequency determination of the same set of shell compositions. In general, as PEG

molecular weight increases, resonance frequency decreases and cavitation threshold

increases. Additionally, all the points from the aforementioned data set collapse onto a

single asymptotically decreasing curve. The trend line is drawn as an aid to the eye.

In Figure 5.10, the previously measured inertial cavitation threshold (PT50) of set a of microbubble shell compositions ranging from 1 – 15 mole% DSPE-PEG, and PEG molecular weights of 1000, 2000, 3000, and 5000 g/mol is plotted against the experimental results from the resonance frequency determination of the same set of shell 155

compositions. In general, as PEG molecular weight increases, resonance frequency decreases and cavitation threshold increases. Such a trend is expected and not especially noteworthy. What is remarkable about the data is the fact that all of the data – from a

wide range of compositions – fall onto a single curve. This finding provides a key insight

as to how shell composition influences cavitation via changes in resonance frequency, as

discussed later.

5.7 Effect of Shell Mass

The changes in resonance frequency as a function of shell composition are likely driven by changes in the stiffness of the microbubble shell. This hypothesis is supported by the results obtained when the measured data is plotted as resonance frequency versus PEG composition for each PEG molecular weight (Figure 5.6). Several trends – albeit with a few exclusions – can be observed in the data. First, increasing the PEG composition significantly decreases the resonance frequency for all molecular weights except PEG

1000. Additionally, an increase in the molecular weight also decreases the resonance frequency. One explanation for these findings is trivial, namely the increase in microbubble mass that accompanies an increase in either PEG molecular weight or PEG mole fraction. This is because resonance frequency (ωr) is directly proportional to stiffness (k) and inversely proportional to mass (m) [35]:

= (Equation 4.5) 2 푘 휔푟 푚 156

Thus, a decrease in resonance frequency can potentially be explained by an increase in

stiffness or an increase in mass or both. In this work changes in mass do not account for

the observed changes in resonance frequency. This can be proven simply by calculating

the stiffness from theoretical mass and a measured resonance frequency. Theoretical

shell mass can be calculated simply with the following relationship:

= ( ( ) + (1 )( )) (Equation 4.6) 푁퐿 푚 푁퐴 푃 푀푊푃 − 푃 푀푊퐿

where NA is Avogadro’s number, P is the mole fraction of polymer in the shell, MWP is

the molecular weight of the polymer functionalized lipid, MWL is the molecular weight

of the lipid, and NL is the number of lipids on a single bubble. NL is calculated to be

about 5 million molecules assuming an average microbubble radius of 1.1 µm (and

therefore surface area of 3.8*10-12 m2), and the surface area of a lipid to be 7.6*10-19 m2.

If changes in the measured resonance frequencies are due only to the change in the shell

mass resulting from increasing PEG mole fraction and molecular weight, then a single calculated stiffness should predict all the experimental results. However, as shown below in Figure 5.11 A, B, a single stiffness predicts higher values for the resonance frequency than the measured values.

157

6000000 A 5500000

5000000

4500000

4000000

3500000

3000000 Resonance Frequency Resonance Frequency (Hz)

2500000 1 3 5 7 9 11 13 15 PEG Composition (%)

8000000 B 7000000

6000000

5000000

4000000

3000000

2000000

Resonance Frequency Resonance Frequency (Hz) 1000000

0 1000 1500 2000 2500 3000 3500 4000 4500 5000 PEG MW (g/mol)

Figure 5.11: Expected resonance frequency based on shell mass. A shows the prediction of the

microbubble resonance frequency for populations consisting of DSPC and 1 – 15 mole%

DSPE-PEG 2000 with constant stiffness. The stiffness calculated from the 1 mole% sample

is applied to the remaining mole fractions (dotted line), in which it predicts values of

resonance frequency higher than the measured values (♦). B shows the predictions of

resonance frequency for microbubble populations consisting of DSPC and 5 mole% DSPE- 158

PEG, molecular weights 1000 – 5000 g/mole. Again, the stiffness calculated from the PEG

1000 sample is applied to the remaining molecular weights (dotted line), in which it

predicts values of resonance frequency higher than the measured values (♦ ).

The observed resonance frequencies are in all cases much smaller than the values expected based solely on changes in mass; that is, without allowing for any change in stiffness. Moreover, the discrepancy between the observed values and the expected values - based on changes in mass alone – grows in magnitude with increasing mass.

Taken together, these results point to changes in stiffness as the primary means by which

PEG influences microbubble resonance frequency, with mass accounting for only a small portion of the decrease in resonance frequency.

5.8 Conclusion

The results of this study suggest that microbubble resonance frequency exhibits significant sensitivity to changes in microbubble shell composition. Until now, similar studies have focused on commercially available contrast agents, and this result – while expected theoretically - has not been demonstrated for the given systems experimentally.

The results can be explained by the Hoff model which quantifies resonance frequency - through attenuation - in terms of rigorous material properties, namely shear modulus and shell viscosity. This work suggests that using shell composition to tune the microbubble resonance frequency to a desired value is feasible within the range of 1 – 8 MHz.

159

The ability to tune the microbubble resonance frequency is of potential significance, given that microbubbles emit specific non-linear signals when responding to sound close to their resonance frequency [28, 67, 96]. These backscattered responses contain not only the transmitted frequency, but harmonics as well. For this reason, microbubbles are useful in harmonic imaging or phase inversion ultrasound, and provide excellent contrast between blood and tissue. By tuning the resonance frequency towards the transmitted ultrasound frequency, one could improve the signal quality of an ultrasound contrast agent formulation. This frequency matching can be of particular importance to ultrasound clinicians, who typically use transducers with frequencies ranging from 1 – 15

MHz depending on the application, image location, and patient. Additionally, it is

likely that tuning the microbubble resonance frequency in this way could also improve efficacy in applications involving microbubbles as triggers for delivery vehicles as occurs in sonoporation and drug/gene therapy.

Utilization of the microbubble resonance frequency data requires an understanding of the

extent to which physical properties influence the value. Therefore, several aspects of this

work warrant further discussion. One is the effect of microbubble size polydispersity and

concentration within a defined composition on the shape of the attenuation profile. While

each case exhibits a resonance frequency value at a clearly defined maximum of total

attenuation, the peak can be altered in amplitude and broadness. That is, the breadth of

the peak can be increased by increasing the polydispersity of the microbubble population

and the amplitude can be increased by increasing the microbubble concentration. A

thinner peak can be obtained simply by formulating a more monodisperse microbubble 160

population, like those prepared from microfluidic techniques [78]. However, it is important to bear in mind that the size polydispersity (for a given average size) of a population of microbubbles only affects the breadth of a given microbubble attenuation

profile but does not account for shifts in attenuation maximum value – thus the resonance

frequency. The same can be said of changes in microbubble concentration. While

increasing the concentration of microbubbles in the sample chamber increases the

magnitude the attenuation, the maximum remains at the same frequency. Therefore, the

measured changes in resonance frequency must be due to some feature of the

microbubble other than size distribution which is sensitive to compositional changes;

most likely this feature relates to the material properties of the microbubble shell.

Another trend is the anomalous increase in resonance frequency at 7.5 mole% PEG –

relative to 5 and 10 mole% - for all molecular weights except PEG-5000, which

subsequently leads to a sharp decrease in resonance frequency followed by a region of

insensitivity to the PEG composition. Note that this value of PEG mole% nearly matches

previously published value of the saturation of PEG 2000 in PEG-lipid membranes, 8

mole% [26, 73, 74]. At mole fractions exceeding the saturation limit, excess PEG

functionalized lipids are thought to self-assemble into micellar structures, which would

not be echogenic or detected by the pulse inversion technique applied in this study [79,

80]. Between alterations in the PEG composition and molecular weight, these results

point to changes in membrane stiffness as the primary parameter controlling the

measured resonance frequency of a microbubble population.

161

This interpretation is tested by invoking the aforementioned Hoff modification of

Church’s equation, which describes sound attenuation through a field of microbubbles as

a function of shell properties. The Hoff model operates under four important

assumptions, however. The model assumes that the shell viscosity and shear modulus are

constant for a given sample, and that the microbubble oscillates isothermally. It is

additionally assumed that the ratio between the shell thickness and bubble radius is

constant. In Hoff’s work, this is a significant assumption, as the shell thickness of the

polymer shell commercial contrast agent studied (Nycomed) has variable shell thickness.

Because of the synthesis method of Nycomed, the shell thickness was not constant, and

was in fact a function of the initial radius. On the other hand, this work uses lipid

monolayer microbubbles, which will have the same shell thickness regardless of initial

radius (length of DSPC molecule), so the shell thickness is constant for a given DPSC-

PEG molecular weight. The shell thickness would however change as a function of PEG molecular weight, as mentioned earlier.

The final, more questionable assumption is that the effect of surface tension is neglected.

The addition of surfactants will lower the surface tension below the value for air/water

(72 mN/m). Recent studies have shown that nonlinearities resulting from the microbubble shell can result in shifts in both the surface tension and resonance frequency

[36, 85]. In Marmottant’s model, the surface tension changes non-linear into three regimes (buckling, elastic, and ruptured) depending on the magnitude of the microbubble oscillations. Overvelde continues with Marmottant’s model to show that the value of the simulated resonance peak is shifted depending on which regime the current microbubble 162

oscillation is in. However, this system operates at a very low acoustic pressure, where microbubble oscillations are predicted to be small exist solely in Marmottant’s elastic region (constant surface tension). At 10 kPa or below, changes in surface tension are sufficiently small that the effect on the magnitude of the oscillation and the resonance peak are negligible. Therefore, in the case of using such a low pressure, the Hoff model can be used with confidence.

This model explicitly accounts for two properties of the shell, namely the shell viscosity and the shear modulus, and describes the total attenuation as a function of frequency and size distribution. However, as the equation does not account directly for the resonance

frequency of the shelled microbubble, it can be inferred by defining it as the minimum

value of attenuation within the relevant range of the experiments (1 - 12 MHz). As a two

parameter model has been used to generate the theoretical resonance frequencies, a

unique solution cannot be arrived upon for the shear modulus and shell viscosity of a

given microbubbles composition; nevertheless, the model predictions agree with the

experimental results using reasonable values of the shear modulus and shell viscosity.

The lines of best fit values arrived at in Figure 4.7 can be further limited by comparing

them with previous research on commercial contrast agents. In Hoff’s work [9], for the commercial contrast agent Nycomed (Nycomed Amershan, Oslo, Norway) he finds that the shear modulus is between 10.6 – 12.6 MPa and the shell viscosity is between 0.39 and

0.49 Pa s. This range of data is supported by several of the best fit lines.

163

Another observation that can be drawn from Figure 5.9 is that each best fit line spans the entire range of shell viscosities input (0 – 2 Pa s) for every PEG composition of the PEG-

2000 molecular weight. However, the best fit lines span a much smaller range of the input shear moduli, between 0 – 50 MPa of the input 0 – 100 MPa. This can indicate that either a relatively large range has been input for the shear modulus or that the resonance frequency is more sensitive to changes in shear modulus than in shell viscosity. It is concluded that the tunability of microbubble resonance frequency has been demonstrated experimentally by altering the shell composition, and experimental results agree with an established model of microbubble physics for this situation.

The utility of this tunability in resonance frequency becomes apparent when one studies carefully Figure 5.10. As noted above, all of the resonance frequency data fall onto a single curve, revealing that there is a unique relationship between inertial cavitation threshold and resonance frequency. It is not the microbubble composition per se that influences cavitation behavior but rather the resonance frequency that results from that composition. On the one hand, this means it is possible to prepare formulations with similar resonance frequencies – and thus similar cavitation thresholds – using different compositions (as occurs in the middle region of Figure 5.10; one can achieve similar results with PEGs of differing molecular weights by compensating with differing PEG mole fractions). On the other hand (near the extremes of Figure 5.10), particular cavitation thresholds can only be achieved with particular compositions (e.g., the highest cavitation thresholds – those greater than 1 MPa - are only accessible with the higher

PEG molecular weights because only these yield microbubbles which are sufficiently 164

stiff). These findings are not only scientific interesting, they are clinically relevant. This

is because avoiding cavitation is necessary during imaging and sonoporation applications

so as to avoid cell (and perhaps patient) death, whereas achieving cavitation is necessary

during drug delivery so as to achieve rupture of the microparticle that carries the drug.

Figure 5.10 shows a simple way of achieving either of these competing requirements; one

can either avoid or ensure cavitation simply by tuning the cavitation threshold pressure -

with appropriate amounts of the appropriate molecular weight of PEG - to be either above

or below the applied acoustic pressure, respectively.

The effect of variations in microbubble shell composition on the microbubble resonance

frequency is demonstrated through experiment. Here, these variations are achieved by altering the mole fraction and molecular weight of functionalized polyethylene glycol

(PEG) in the microbubble phospholipid monolayer shell, and measuring the microbubble resonance frequency. The resonance frequency is measured via a chirp pulse and identified as the frequency at which the total attenuation of sound wave is the greatest while in the presence of microbubbles. For the shell compositions utilized herein, the resonance frequency varies significantly from 1 – 8.15 MHz. This change in resonance frequency is shown to not be a function of simply the changing mass of the microbubble shell, but related to some change in the shell stiffness. To further confirm the experimental data and explain the changes in stiffness, the measured resonance frequencies are compared with theory, namely through Hoff’s modification of Church’s equation, using shear modulus and shell viscosity as tuning parameters. It is concluded 165 that the design and synthesis of microbubbles with a prescribed resonance frequency is attainable simply by tuning PEG composition and molecular weight.

166

CHAPTER 6: Co-encapsulation Ultrasound Contrast Agent

6.1 Co-encapsulation Introduction

Thinly shelled acoustic microbubbles are typically used in providing contrast to ultrasound images. When insonified, these microbubbles tend to oscillate at the driving frequency of ultrasound, contracting during the positive pressure cycle and growing larger than the resting radius during the negative pressure cycle [12, 29, 65]. While the driving frequency of ultrasound controls the speed of these oscillations, the magnitude of the oscillations is controlled by the overall pressure of the sound wave. If the peak negative pressure is increased sufficiently and the microbubble expands past a critical radius, it will implode and create a localized shockwave and increase in temperature and pressure [38, 65]. This so-called inertial cavitation of microbubbles has become increasingly interesting to contrast imaging and drug delivery researchers in a variety of ways [13, 25, 41, 64, 97]. The phenomenon is interesting in the imaging field as increasing the mechanical index (MI) of a clinical transducer above a certain threshold will also cause the destruction of the contrast agent, and potential cellular damage [38,

98]. Commercial contrast agents were given the Food and Drug Administration’s black box label in 2007 due to a death during cardiac imaging enhanced by contrast agents [99].

While it is uncertain whether the mortality was a direct result of the addition of contrast

or the result of a pre-existing condition, there is merit in the development of a contrast

agent with a safer design, by way of controlling or containing inertial cavitation. 167

The goal of this chapter is to develop a novel contrast agent taking into account the inherent danger of microbubble inertial cavitation. While this idea is not new to the medical imaging community [20, 100], the novel aspect of this research focuses on the co-encapsulation of stable, solid phase, phospholipid-shelled microbubbles within the aqueous core of a polymer shell microcapsule. The potential advantage of this contrast agent is the addition of the encapsulating polymer shell to shield the lipid shelled microbubbles within from the acoustic field. By controlling the acoustic pressure (or MI) of the ultrasound wave, the cavitation behavior can be controlled and thus the safety of the contrast agent, given that microbubble inertial cavitation is the potential hazard of ultrasound imaging. Additionally, the polymer shell can potentially increase the lifespan of a circulating microbubble as well as render it more difficult to inertially cavitate.

Commercial contrast agents can last up to 42 minutes after synthesis in an air-enriched environment, or several minutes circulating through the bloodstream; however, when microbubbles are exposed to ultrasound at typical clinical imaging MI values, microbubble contrast agents can last only seconds regardless of their location [6, 101].

The proposed contrast agent has benefit of longer lasting contrast by either shielding the co-encapsulated microbubbles from low pressure ultrasound waves, or trapping the gas within the shell to hinder gas dissolution. Thus, by controlling the peak negative pressure of transmitted ultrasound, the proposed contrast agent can be used to increase both safety and longevity of the acoustically active microbubbles within.

168

Polymer microcapsules are not limited to contrast applications, and are more commonly

employed in the field of drug delivery [102]. These microcapsules are favorable because of their size flexibility and ability to carry both a relatively large volume of encapsulated drug. As mentioned earlier, inertial cavitation of co-encapsulated microbubbles may be used as a potential drug release trigger as well. In tissue engineering, polymer microspheres have also been used to affect the mechanical properties of implants and biomaterials [103]. Both of these applications would potentially be bolstered by the ability to determine the location of the polymer microspheres by their echogenicity, whether in the blood or a biomaterial. Because of the existence of a wide array of uses for polymer microspheres, there are potentially unforeseen applications for the implication of acoustically active microcapsules. However, this chapter focuses largely on the application of the co-encapsulated microbubbles as a contrast agent.

6.2 Design of Co-encapsulated Contrast Agents

6.2.1 Materials

Poly(L-lactic Acid) (PLA) and Polyvinyl alcohol (PVA) were supplied by MP

Biomedical (Solon, Ohio). The PLA polymer is reported to have a FW of 100,000, and an inherent viscosity of 1.61 dL/g. The polyvinyl alcohol used for emulsifying has a molecular weight of ~27,000 g/mol and is reported to be 99% hydrolyzed. The PVA used for the phantom synthesis has an average molecular weight between 85,000 and

124,000 g/mol and is 98-99% hydrolyzed. The lipid 1,2-Distearoyl-sn-Glycero-3- 169

Phosphocholine (DSPC) and the functionalized lipids 1,2-Disteroyl-sn-Glycero-3-

Phosphoethanolamine-N-[Methoxy(Polyethyleneglycol)-5000 (and 2000)] (DSPE

PEG5000, or 2000) were purchased from Avanti Polar Lipids (Alabaster, AL). Sulfur

Hexafluoride (SF6) was purchased from Airgas (Allentown, PA). Fluorinated lipid 1,1’-

dihexadecyl-3,3,3’,3’-tetramethyl-indocarbocyanine perchlorate (DiI-C16) was purchased from Invitrogen Molecular Probes (Carlsbad, CA). All other reagents used were of analytical grade.

6.2.2 Microbubble Preparation

Microbubbles are prepared as described earlier and in previous works [42, 63]. A lipid film containing 95 mole% DSPC and 5 mole% DSPE PEG 2000 (or 5000) was deposited onto a scintillation vial from stock solutions dissolved in chloroform by nitrogen spin drying followed by 2 hours in vacuum. The dried film was then rehydrated with 5 ml of aqueous phosphate buffered saline (PBS) solution (pH 7.4) by sonicating the sample

(Hielscher UP200S Ultrasonic Processor, Hielscher, Tetlow, Germany) for 3 minutes at

20% amplitude. This has the dual effect of dissolving the lipid mixture in solution and raising the temperature above that of the lipid’s gel phase transition temperature, 55 oC.

The rehydrated solution is then aliquoted out into 2 ml serum vials and sealed. The head

space air is then evacuated from the vial and replaced with the heavy gas, SF6. Finally

the vials are vigorously shaken using the Vialmix shaker (Lantheus Medical Imaging,

North Billerica, MA) in order to disperse the gas phase. The resultant microbubbles are

allowed to settle at room temperature for 30 minutes, however long term storage should 170

be at 2-8 oC. These techniques successfully produce stable microbubbles with a 1-2 µm

diameter, shown in Figure 6.1 A.

Figure 6.1: Contrast agent micrographs. Light microscope images are presented for typical batches of:

A Microbubbles with DSPC/ 5% DSPE PEG 2000 shell around SF6 gas, B PLA

microcapsules, C PLA microcapsules with co-encapsulated DSPC microbubbles.

6.2.3 Microcapsule Synthesis

PLA microcapsules are prepared using the well characterized water/oil/water (W/O/W)

double emulsion technique described previously and modified for effectiveness [104-

106]. A schematic of the W/O/W double emulsion process is detailed below in Figure

6.2.

171

Figure 6.2: W/O/W double emulsion. The double emulsion technique is diagramed to explain a

successful method of encapsulating microbubbles within the aqueous core of a microcapsule.

First, a relatively small volume of aqueous media (here, microbubbles in PBS) is added to a

larger (10 times) volume of an organic (DCM) with dissolved polymer (PLA). This mixture

is homogenized for 1 minute, then added to an even larger (8 times) volume of water plus an

emulsifier (PVA). This mixture is homogenized for 2 minutes and the resulting emulsion is

left to dry overnight. This process results in polymer microspheres encapsulating the first

aqueous phase (microbubbles in PBS), in a solution of the second aqueous phase (water with

PVA).

A solution of 0.2 ml of the above microbubbles suspended in various concentrations in

PBS or 70 mM calcein buffer (internal water phase) is added to 2 ml of 10 mg/ml PLA in dichloromethane (intermediate organic phase). This solution is then homogenized with the Polytron PT3100 homogenizer (Kinematica, Lucerne, Germany) for 1 minute at

15000 rpm in order to create the primary W/O emulsion. Quickly, 16 ml of 2% PVA in water is added to the solution and homogenized at 15000 rpm for 2 minutes, which will serve as the double emulsion W/O/W and the outer aqueous phase, W2. After homogenization, an additional 32 ml of the 2% PVA is added and the mixture is moved 172 to a 400 rpm magnetic stir plate to allow the dichloromethane to evaporate for 24 hrs.

2% PVA is a sufficient dissolved polymer concentration for emulsification. After drying, the solution is washed of the PVA by centrifuging the sample at 15000 xg for 20 minutes.

The supernatant PVA solution is siphoned off and replaced with water or PBS, and the sample is then centrifuge washed twice more. This technique creates stable microcapsules with co-encapsulated microbubbles of diameters between 5-10 µm.

Samples described above of microcapsules with co-encapsulated microbubbles are shown in Figure 6.1 C, while microcapsules prepared with their internal aqueous phase composed of only PBS (no microbubbles) or 70 mM calcein are shown in Figure 6.1 B.

Detailed images of the microparticles can be attained from a scanning electron microscope (SEM) (FEI XL30, FEI, Hilsboro, OR). For SEM imaging, the microparticles are first washed of all PVA solution, which is replaced with water. The solution is then lyophilized. It is necessary for the microcapsules to be in water because when lyophilized any dissolved polymer or salt will deposit on the microparticles. After freeze drying, the microcapsules are then sputter-coated with approximately 10 nm of platinum, for enhancement of the SEM image. A representative SEM image is shown in

Figure 6.3.

173

Figure 6.3: Microcapsule SEM image. SEM image of the double emulsion PLA microcapsules. The

bulk of the microcapsules are between 1 – 10 µm in diameter. Wrinkling and other damage to

the microcapsules is an artifact of the SEM preparation procedure.

Since SEM is a surface imaging technique, it is difficult to prove that microbubbles have successfully been encapsulated within the aqueous core of the microcapsules. A simple proof of concept experiment is therefore designed to determine whether the microbubbles present in the inner aqueous phase of the double emulsion have been successfully encapsulated. Microbubbles are produced with 0.5 mole% DiI functionalized DSPE fluorescent probe, along with 4.5 mole% DSPE-PEG 2000 and 95 mole% DSPC. This way, the microbubbles will be easily identifiable with fluorescence microscopy. The fluorescent microbubbles are then used as the inner aqueous phase of a double emulsion, 174 as described previously. The resultant microparticles are imaged under the Carl Zeiss fluorescence microscope, both under light and under fluorescence only. The results of an imaged particle are shown in Figure 6.4, below.

10 µm

Figure 6.4: Encapsulation of fluorescent microbubbles within double emulsion particles. DiI labeled

microbubbles are encapsulated within polymer microcapsules using the double emulsion

technique and imaged with both light and fluorescence microscopy. The image on the left is

of a microcapsule under white light only, while the image on the right is recorded in

fluorescence mode. The inner fluorescence in the right image is indicative of successfully

encapsulated fluorescent microbubbles.

A single double emulsion particle with encapsulated DiI functionalized microbubbles is displayed above. The image on the left is recorded under only the microscope light. The microscope light is then switched off and the fluorescent lamp is lit without moving the slide, as to record the response from the same microcapsule. Under the excitation wavelength, the microcapsule clearly fluoresces. This degree of fluorescence is indicative of successful co-encapsulation of the DiI functionalized microbubbles, especially because fluorescence is only present inside of the microcapsule captured in the light only image. 175

The capsules displayed in Figure 6.4 are approximately 10 µm in diameter. For the

purposes of this study, microcapsules of approximately 5 µm are preferable, especially

because they are sufficiently small to fit through the size of the smallest capillary in vivo

[16]. However, it is quite simple to synthesize microcapsules of various sizes through

several methods. First, increasing homogenization speed (for the second emulsion)

decreases the size of the particles. Additionally, increasing the hydrophobicity of the

organic phase leads to an increase in final particle size. While larger microcapsules

would not be clinically relevant, they may be of some interest for purely scientific

studies, such as studying the cavitation behavior or acoustic response of the encapsulated

microbubbles.

The concentration of microparticles was measured with a Beckmann-Coulter Z1 Particle

Counter (Beckmann-Coulter, Brea, CA). The Z1 particle counter measures the

concentration of particles with a size larger than 2 µm, and shows how many are above a

set threshold value. For a typical batch of microparticles described above, the coulter

counter reports a concentration of 120*106 microparticles/ml (assuming that the batch

which started with 0.2 ml of inner phase is concentrated to a final volume of 1 ml after

centrifugation). From the threshold values, the coulter counter also reports that 83% of the total microparticles measured are between 4 – 8 µm. Higher concentrations of

microparticles, like those required in Section 6.5, can be attained by successive

centrifugations of a larger batch of microparticles and subsequently concentrating them to

the same final volume (1 ml). 176

6.3 Clinical Imaging of Contrast Agents

To test the echogenicity of the contrast agent, samples are first imaged by two clinical

ultrasound units. The contrast agent, consisting of double emulsion microcapsules with

co-encapsulated microbubbles, is shown to be visible in B-mode at a low MI of 0.4, while freely floating in a water tank, shown in Figure 6.5. Figure 6.5 was imaged a Toshiba

Nemio XG (Toshiba Medical Imaging Co., Tochigi, Japan) with a 12 MHz transducer.

Figure 6.5: Brightness mode ultrasound image of microcapsules with co-encapsulated

microbubbles. A 6 MHz transducer is held in a large tank of normal saline, and the sample is

injected at the equivalent of the bottom left of the image. The mechanical index of ultrasound

is 0.4. Microcapsules are observed flowing into the image from the point of injection.

177

Even from this snapshot it is evident that this co-encapsulated contrast agent formulation provides some contrast to the ultrasound image. However, signal intensity is only part of functionality of an ultrasound contrast agent. A successful contrast agent should also be

evaluated for its longevity under an ultrasound field. Because of the polymer

microcapsule shell encapsulating the bubbles, it is logical to assume that the co- encapsulated formula should provide some degree of protection for the bubbles encapsulated within. This can either be attributed to added reflections of the incident sound wave of the latex/water interface of the sample chamber, or due to the inability of the microbubble to dissolve while entrapped within the polymer shell. Figure 6.6 shows the quantified results of an experiment designed to test the longevity of the co- encapsulated contrast agent against the current United States industry standard contrast agent, Definity (Lantheus Medical Imaging, North Billerica, MA), over 30 minutes of constant imaging with the aforementioned Toshiba machine. The shell composition of the Definity contrast agent is very similar to the formulation of the microbubbles prepared in Section 6.2.2 (albeit a more complex mixture), such that the shell is a lipid monolayer with some percent of the lipids being functionalized with a stabilizing polymer. Definity is further stabilized in a viscous solution (glycerin rich) and the encapsulated heavy gas is octafluoropropane.

178

Figure 6.6: Normalized acoustic brightness of contrast agents. The co-encapsulated contrast agent (♦)

and a commercial contrast agent (Definity(▲)) are imaged on a Toshiba clinical ultrasound

unit for 25 minutes with a 12 MHz transducer. The normalized results show that Definity has

a higher decay rate of its acoustic brightness intensity than the co-encapsulated formula, by

approximately a factor of 2.

The results in Figure 6.6 have been normalized with their initial brightness to quantify

their longevity. The co-encapsulated contrast agent is shown to retain its initial

brightness twice as well as the commercial contrast agent, Definity, over the 30 minute

imaging window. These results are somewhat encouraging; however Figure 6.6 does not provide the whole story. The raw data (before normalization) shows that although

Definity does have a higher decay rate of brightness than the co-encapsulated formula, 179

Definity also has higher brightness intensity initially and throughout the experiment than the co-encapsulated contrast agent. The raw data is provided below in Figure 6.7.

30

25

20

15 Particles

Brightness Definity 10

5

0 0 5 10 15 20 25 30 Time (min)

Figure 6.7: Raw acoustic brightness of contrast agents. In contrast to Figure 6.6, the raw acoustic data

is provided here for both Definity and the co-encapsulated contrast agent. Although Definity

has the higher decay rate, it also provides a higher degree of brightness initially and

throughout the imaging time. The brightness of Definity finally matches the initial brightness

of the co-encapsulated formula after the full length of the scan, 25 minutes.

To further confirm the brightness resulting from encapsulated microbubbles and not from reflection or scatter off the interface of the microcapsule, samples of pure microbubbles, double emulsion particles without co-encapsulated microbubbles, and the double 180

emulsion particles with co-encapsulated microbubbles are viewed with a phase inversion

mode on the Siemens Acuson Antares (Siemens, Berlin, Germany). Additionally, the

samples are imaged within an agar gel phantom prepared with a 12 mm diameter, 10 mm deep cavity in the center. A 1 ml aliquot of sample is poured into the cavity and covered by 1 cm thick agar cylinder, and a convex 2-6 MHz transducer is positioned on top.

Figure 6.8 A-F shows the images from the three samples immediately after transducer activation and 3 seconds into imaging at a frequency of 2.5 MHz, where the square window in the center is enhanced by tissue harmonic imaging.

Figure 6.8: Tissue harmonic images (THI). THI are shown from the three samples within an agar gel

phantom immediately after transducer activation and 3 seconds into imaging at an MI of 1.5

and frequency of 2.5 MHz, where the square window in the center is enhanced by THI. A

microbubbles after a millisecond of ultrasound, B microbubbles after 3 seconds of

ultrasound, C microcapsules without microbubbles at 1 ms, D microcapsules after 3 s, E 181

microcapsules with co-encapsulated microbubbles at 1 ms, F microcapsules with co-

encapsulated microbubbles after 3 s.

Comparing the figures it is evident that the pure un-encapsulated microbubbles (Figure

6.8 A-B) give the strongest response, microcapsules with no microbubbles (Figure 6.8 C-

D) give the weakest or no response, and the microcapsule vehicle with microbubbles

(Figure 6.8 E-F) gives some signal. The difference in the overall brightness of the sample of microbubbles (Figure 6.8 A) compared to the sample of microcapsules with microbubbles (Figure 6.8 C) is expected since the concentration of overall microbubbles is at least 1000 times less in the sample of microcapsules with microbubbles; however an individual microbubble appears to give a similar brightness in both samples. After 3 seconds of harmonic imaging the un-encapsulated bubbles are disappearing from the image (Figure 6.8 B), which could be from dissolution due to high MI of imaging, equivalent to a peak negative pressure of 2.4 MPa. However, the sample of microbubbles encapsulated within microcapsules (Figure 6.8 F) shows little change over the 3 seconds of ultrasound imaging.

6.4 Acoustic Response of Contrast Agents

As a method of quantifying the amount (or existence) of microbubble activity of the co- encapsulated contrast agent, the acoustic response of a sample can be analyzed.

Specifically, the co-encapsulated contrast agent should be compared to a sample of microbubbles which have not be encapsulated, as well as microcapsules which have no 182

microbubbles encapsulated. As in Chapter 3, the acoustic response can be detected by

the SchaumSchläger, a homemade high voltage pulser designed by Michał Mleczko,

described earlier and in previous research [63, 66, 71], driving a 2.25 MHz, 7.5 cm focus

ultrasound transducer (Olympus NDT, Waltham MA). Another 2.25 MHz transducer is

set at 90o to the transmitter and receives the acoustic response of a sample insonified by

the transmitting transducer, such that the overlap of the foci of the two transducers is a 1

mm3 volume. The experiment consists of short bursts of 50 pulse trains, which are

transmitted at a repetition frequency of 5 Hz, followed by 1 minute of rest, then repeating

the 50 pulse train burst every 30 seconds. The peak negative pressure of the sound is

2.15 MPa. The sample chamber is stirred by a magnetic stir plate at 600 rpm set under the tank. The received signal is filtered to reduce noise by a 5 MHz low pass filter

(Minicircuits, Brooklyn NY) and amplified by +26 dB (Panametrics NDT, Waltham MA)

before being digitized by an oscilloscope (Cleverscope Ltd., Auckland NZ). The signal is

then processed by MATLAB such that the total voltage response magnitude will be

plotted against the overall time of the experiment.

183

Figure 6.9: Acoustic response graphs. The responses are generated from the three contrast agent

samples generated by a 2.25 MHz transmit/receive system. The received voltage (in volts) is

plotted against the experiment time (in seconds). A Response from samples of microcapsules

alone (■), which appears as only noise, and from microcapsules with co-encapsulated

microbubbles (♦), which show an exponential decrease in acoustic activity. B Response from

the sample of microbubbles only.

184

The results of the microbubble detection method are shown in Figure 6.9 A-B for samples of the same formulations as above. Concentrated un-encapsulated microbubbles

(Figure 6.9 B) again confirm the highest ultrasound response with an initial measurement of 9 mV, and all microbubble response is negated by either cavitation or dissolution by

200 s. The sample of microcapsules with no encapsulated microbubbles (Figure 6.9

A[■]) confirms that only noise level acoustic response is present in the sample, with µV measurements throughout the time period of the experiment. The sample of microcapsules with co-encapsulated microbubbles (Figure 6.9 A[♦]) initially shows a high response of 0.35 mV, but quickly returns to the noise level, indicating that any microbubbles present in the microcapsules have disappeared or changed so that they are no longer acoustically active.

This simple technique for measuring the acoustic response of contrast agents can also be

implemented to examine a range of situations. One such study of interest is measuring

the shelf life of contrast agents once they have been synthesized. This can be achieved

by measuring the acoustic response of the contrast agents over a one month period. Since

it is of interest to prove that the co-encapsulate formula provides some degree of protection for its encapsulated microbubbles, it is expected that its acoustic response will retain its value longer than that of un-encapsulated microbubbles. The un-encapsulated microbubbles in this case are comprised of 5 mole% DSPE-PEG 2000 and 95 mole%

DPSC, and mimic commercially available contrast agents, such as Definity or SonoVue.

The results of the 30 day acoustic response study are shown in Figure 6.10, below.

185

1.8

1.6

1.4

1.2

1

Particles 0.8 Bubbles

Acoustic Response 0.6

0.4

0.2

0 0 5 10 15 20 25 30 35 Time (Day)

Figure 6.10: Shelf life of synthesized contrast agents. The shelf life of contrast agents is determined

by measuring the acoustic response of the contrast agent sample over a 30 day window, and

normalizing the results with the respective initial acoustic response value. The co-

encapsulated contrast agent [♦] proves to retain it s acoustic response very well over the 30

day period, losing only 40% of its initial response. On the other hand, un-encapsulated

microbubbles [■ ] quickly lose almost all their response (99%) only a few days after

synthesis.

The results of the study prove that in fact the co-encapsulated formula provide a significant increase in shelf life versus un-encapsulated microbubbles. This is most likely due to the polymer shell trapping the heavy gas from dissolving or returning to the atmosphere. As with the results of the brightness study undertaken in Section 6.3, these results have been normalized with their respective initial values of acoustic response. In 186

this study, analysis of the raw data reveals that the total acoustic response of the un-

encapsulated microbubbles is only higher than the acoustic response of the co-

encapsulated contrast agent on day 1, than equal to each other on day 2, and finally the

acoustic response of the microbubbles is less than that of the co-encapsulated contrast

agent on days 3-30. This data only serves to reinforce the previous result; by analysis of

both normalized and raw data, the co-encapsulated contrast agent has proven to have a

longer shelf life after synthesis than a population of microbubbles with an initially higher

acoustic response.

Another way the acoustic response can be employed is to determine the acoustic

relationship between concentrations of microbubbles and microparticles. A major

challenge in relating the acoustic concentration of contrast agents is the inconsistency in

the amount of non-linear oscillators (microbubbles) per ml of dosage. For contrast agents

which are simply comprised of a population of microbubbles, this is a straightforward

calculation. However, in complex case of the co-encapsulated contrast agent described

here, relating the acoustic concentration of the un-encapsulated microbubbles to the same microbubbles which have been co-encapsulated is not simple. Simply knowing the amount of microcapsules per ml is insufficient information to relate the acoustic concentration. This is because the amount of microbubbles encapsulated within a given microcapsule is not constant from microcapsule to microcapsule. In fact, the number is impossible to tell, and in some cases there may not be any microbubbles encapsulated.

This can be attributed to the chaotic fashion in which the microbubbles are encapsulated, the random homogenization step of the double emulsion. The double emulsion technique 187 results in poor loading efficiencies (reported by Kashi as 4.7% for drug molecules [107]) because of the interaction between the inner aqueous phase and the outer aqueous phase during the secondary emulsion. Because of these factors, the acoustic concentrations of the aforementioned contrast agents should be determined empirically by analyzing their acoustic response. In this study, various concentrations of microbubbles (un- and co- encapsulated) are measured for their acoustic response from a 40 pulse train signal with

PNP of 2 MPa. The results are displayed below in Figure 6.11.

0.02

0.015

0.01 Particles Bubbles Acoustic Response

0.005

0 0 200 400 600 800 1000 1200 Respective Concentration

Figure 6.11: Concentration effects on the acoustic response of contrast agents. Various

concentrations of un-encapsulated [■ ] and co-encapsulated [♦] microbubbles (5 mole%

DSPE-PEG 2000, 95 mole% DSPC) are measured for their acoustic response. The

concentrations of un-encapsulated microbubble range from 0.1 to 200 microbubbles per ml, 188

and the concentration of co-encapsulated microbubbles ranges from 10 – 1000 µl of

synthesized solution. Both sample display a linear increase in the acoustic response with

increasing concentration (although the concentration of one contrast agent cannot be

compared to the concentration of the other directly).

Figure 6.11 shows a linear increase in both contrast agent samples with increasing

concentration. The un-encapsulated microbubble range from concentrations of 0.1 to 200

microbubbles per ml, and the co-encapsulated microbubbles ranges from concentrations of 10 – 1000 µl of synthesized solution. Obviously, these concentration values cannot be directly related because of the factors discussed earlier. In order to compare apple and oranges (here, un- and co-encapsulated microbubbles), more data is needed. It is of

interest to develop an empirical scaling factor which can “convert” the amount of

microcapsules equaling the brightness of a microbubble. Armed with such a conversion

factor, future studies can adequately predict the encapsulated concentration of

microbubbles within polymer microcapsules. This is especially important when

comparing the co-encapsulated formula to any other contrast agent, whether analyzing

acoustic response, brightness, cavitation threshold, cytotoxicity, or any number of

unforeseen studies. This conversion factor will be explored using a more rigorous

contrast parameter, the contrast to tissue ration.

6.5 Contrast to Tissue Ratio

189

Although the raw acoustic response data can be used to confirm encapsulation of

microbubbles within the aqueous core of a polymer microcapsule, a more scientific and

clinically relevant result is desirable for studying contrast parameters. To analyze the

degree of contrast that an ultrasound contrast agent will provide, the brightness (or

intensity) of the image should be compared to the brightness of some reference material

(Equation 6.1, where Ic and It are the brightness intensities of the contrast region and

tissue region, respectively). For physiological relevance, this reference material should

have similar acoustic properties to human flesh (1540 m/s speed of sound, 1400 kg/m3

density). While actual human flesh is somewhat difficult to legally attain, a tissue mocking phantom with the aforementioned acoustic properties can be easily fabricated without criminal repercussions.

= 20 log 퐼푐 퐶푇푅 � � 퐼푡 (Equation 6.1)

The tissue mocking phantom is comprised of a 10 weight% PVA solution, which is

subjected to multiple freeze thaw cycles to alter the acoustic properties, a technique

adopted from Surry [108]. A 3 L solution of 10 w% PVA is autoclaved for 2 hours to

fully dissolve the polymer. After the PVA is fully dissolved, the solution is poured into

the phantom mold, a 3.5 L steel box with a cylindrical cavity, and is left for 1 day to

allow trapped gas to separate from the solution. The mold is then subjected to 3 freeze

thaw cycles such that the phantom is completely frozen (to -20 oC) and completely

thawed (to 20 oC) in a 24 hour time period. The freeze thaw cycles serve to realign the 190 crystal structure of the PVA such that the polymers align into tighter stacks with increasing freeze thaw cycles. Acoustically, the speed of sound and density both increase with increasing number of freeze thaw cycles, and after 3 cycles the acoustic properties closely match that of flesh [108]. The phantom should be stored at 2-8 oC in deionized water to avoid dehydration of the cryogel phantom. Now the contrast agent brightness intensity can be compared to that of the tissue mocking phantom, and a dB scale of the intensities can measured as a contrast-to-tissue ratio (CTR).

Figure 6.12: Contrast to tissue ratio phantom. To determine the CTR, the PVA phantom is insonified

with a curved array ultrasound transducer. The phantom has a 40 ml cylindrical cavity

which is filled with the contrast agent solutions, held within a latex ultrasound probe cover.

The resulting brightness of control volumes within the cavity (contrast zone) and the

phantom (tissue zone) can be compared to calculate CTR.

The contrast to tissue ratio of a given population of contrast agents is determined by recording brightness (B) mode and phase inversion ultrasound images and then analyzing 191 their intensities. Samples are placed a 40 ml reservoir within a larger block of PVA cryogel phantom. The reservoir is imaged from the side of the phantom with the

Ultrasonix Sonix RP (Ultrasonix, Richmond, BC) and a 3.5 MHz curved array transducer

(C5-2/60), the process displayed in Figure 6.12. The resulting image is analyzed by comparing the intensity of a control volume within the reservoir area (contrast zone) to the intensity of a control volume of the phantom (tissue zone). The experiment lasts a total of 10 seconds, with a one image per second frame rate, and is repeated for 6 MIs ranging from 0.23264 – 1.4808 in both B-mode and phase inversion mode.

Figure 6.13: Phase inversion mode ultrasound images of co-encapsulated contrast agent. The

experiment is carried out in a 40 ml reservoir within an agar gel phantom. Progressing

images 1-10 illustrate the change in intensity of the contrast agent over a period of 10

seconds, with an MI of 1.4808. While the initial brightness is lost in 4 seconds, the steady

state intensity is still higher than 0, which would be black in color.

To confirm the co-encapsulation of the microbubbles within the aqueous core of the PLA microcapsules, the CTR of the contrast agent is examined. Figure 6.13 shows 10 progressive images taken during the experiment, where each image represents 1 second 192 of ultrasound (MI = 1.4808). After approximately 4 seconds, the initial brightness has faded, which is indicative of some bubbles cavitation or destruction. After 4 seconds the intensity stays fairly consistent for the remaining 6 seconds, however, this intensity is still well above the 0 value for pure water, which would be black on the image. To further quantify the CTR of the co-encapsulated contrast agent, the same experiment was preformed with MIs ranging from 0.23264 – 1.4808, and graphed in dB versus the frame number in Figure 6.14 A (phase inversion mode) and Figure 6.14 B (B-mode).

Figure 6.14: Contrast to tissue ratio of co-encapsulated contrast agent and SonoVue. Images of the

contrast agents are recorded every second (1 frame per second), and the ratio of the

intensity of the contrast agent to the intensity of the tissue (CTR), or in this case an agar gel

phantom, is calculated for MIs between 0.23264 and 1.4808. A Shows the co-encapsulated 193

microbubbles contrast agent in phase inversion mode, and B shows the same sample in B-

mode. The same test is preformed with SonoVue, C shows SonoVue in phase inversion

mode, and D shows SonoVue in B-mode. The increase in CTR between phase inversion

and B-mode is explained by the presence of some non-linear oscillators, which in both

cases are microbubbles. It can also be observed that as expected an increase in MI results

in a sharper decrease in CTR, as microbubbles are being cavitated. Co-encapsulated

microbubbles also show that they exhibit similar acoustic response to the commercial

contrast agent, SonoVue.

The +7 dB increase in intensity between the B-Mode and phase inversion is expected because of the non-linear oscillations of the microbubbles, and helps confirm their existence. The highest MI in Figure 6.14 A, 1.4808, graphically represents the images in

Figure 6.13. Additionally, the intensity drops rapidly with increasing MI and sonication

time. To compare the results of the co-encapsulated contrast agent with one which is

commercially available, the same test is preformed on SonoVue (Bracco, Milan, Italy).

Figure 6.14 C-D show the results of CTR test on SonoVue with the same range of MIs at

a similar concentration. Here, SonoVue reacts similarly to the co-encapsulation CTR test in both its B-mode/phase inversion deviation and its trend with increasing MI.

The CTR can also be used to definitively find the brightness correlation between microbubbles and co-encapsulated microcapsules. In this experiment, the CTR is

measured by the Toshiba clinical ultrasound machine mentioned earlier for both the co-

encapsulated microcapsules and the Definity ultrasound contrast agent. It is assumed that

Definity contains 1 billion bubbles per ml (but probably contains more) and the

microparticle concentration is determined earlier by the Coulter Counter. By 194

successively diluting both samples between 0 and 1 million bubbles/ml, and 0 and 120

million particles/ml, the CTR profile of both contrast agents can be determined at an MI

of 0.4. Figure 6.15 displays both of these CTR profiles with respect to their respective

concentration (Definity: top scale, co-encapsulated contrast agent: bottom scale).

Figure 6.15: CTR of Definity and the co-encapsulated contrast agent. The CTR of both Definity and

the co-encapsulated contrast agent increase logarithmically with increasing concentration.

They increase equivalently with respect to each other, separated by concentration factor of

125 microparticles per microbubble.

Overall, both Definity and the co-encapsulated contrast agent increase logarithmically by

+18 dB with respective concentration. More interestingly, the CTR curves of the contrast 195

agents overlap when adjusting the concentration axis by a factor of 125 microparticles

per microbubble. This factor is of value because it allows for a so-called acoustic relation between the developed co-encapsulated contrast agent and a commercially available one.

The overlap of the curves is also encouraging, as it proves that both contrast agents are mechanistically responding to ultrasound in a similar fashion, albeit separated by two orders of magnitude.

To compliment the brightness data analyzed in Section 6.3, the CTR can also be used to analyze the acoustic brightness of contrast agents over time. Additionally, the CTR can now be normalized experimentally by utilizing the knowledge learned above, namely the particle/bubble conversion factor: 125. The CTR is again monitored with the Toshiba unit for 30 minutes of continuous imaging, with still images captured at regular intervals

at an MI of 0.4. In this experiment, the CTR is compared between the co-encapsulated

contrast agent and against home-made Definity analog microbubbles, with a shell composition of 95 mole% DSPC, 5 mole% DPSE-PEG 3000. The results of the contrast agents’ response to clinical ultrasound imaging over time are displayed below in Figure

6.16.

196

10

5

0 0 5 10 15 20 25 30 35 Co-encapsulation Definity CTR (dB) -5

-10

-15 Time (min)

Figure 6.16: CTR under continuous ultrasound. The CTR of both the co-encapsulated contrast agent

and un-encapsulated microbubbles are compared during 30 minutes of continuous

ultrasound imaging. Images are captured at regular intervals during the sonication. The co-

encapsulated contrast agent retains its contrast longer than the un-encapsulated formula at

an MI of 0.4.

This figure definitively shows that when the initial CTR is identical between the two studied contrast agents, the co-encapsulated contrast agent lasts longer under constant ultrasound imaging. While the un-encapsulated microbubbles decline steadily from the onset of imaging (recalling that dB is a log scale), the un-encapsulated microbubbles experience an initial drop of -4 dB, but retain their positive CTR value of +4 dB for the remainder of the experiment. The steady drop in the un-encapsulated bubbles can be 197

attributed to the microbubbles all making eventual contact with the sound wave, and not yet reaching the CTR of plain water. In the case of the co-encapsulated contrast agent,

the contrast which is initially lost can be attributed to some percentage of the

microbubbles within being cavitated, most likely some portion of the size distribution.

The more resilient encapsulated bubbles are likely shielded from cavitation by the

protection of the polymer shell. With this result, the co-encapsulated contrast agent has proven to last longer under ultrasound than the commercially available ultrasound contrast agent, Definity.

6.6 Cavitation Behavior of Co-encapsulated Microbubbles

6.6.1 Cavitation Measurements

Two inherent advantages of co-encapsulating microbubbles within the aqueous core of a polymer microcapsule are added longevity and increased patient safety. Both of these potentially positive outcomes are derived from the protection of the microbubbles by the

polymer shell. The polymer shell is responsible for some degree of reflections from the

incident sound wave, along with a diffusion barrier for the trapped heavy gas. On the

other hand, the effects of microbubbles which are potentially inertially cavitating within

the microcapsules are retained somewhat from reaching the outside of the polymer shell.

For example this is beneficial for the livelihood of endothelial cells which could

potentially be killed by a nearby inertially cavitating microbubble.

198

If the mechanism of cell death is indeed inertial cavitation, then testing for the inertial

cavitation threshold of the co-encapsulated sample versus only the microbubbles with no

polymer shell is a logical test. If the polymer shell increases the inertial cavitation

threshold of a given composition of microbubble, than the co-encapsulation formula is inherently safer and will remain active longer in a sound field than the typical microbubbles studied before.

A similar experimental set up as described in Chapter 3 is used to determine the cavitation threshold of the contrast agents, described also in previous work [52]. In this case, the transmitter creates pulse trains consisting of 4 pulses of 4 cycles with 80 µs between pulses. Every other pulse is inverted to allow for phase inversion in signal processing. The total experiment consists of 600 pulse trains, which are transmitted at a repetition frequency of 5 Hz. The experiment is repeated for set peak negative pressure amplitudes between 50 kPa and 2 MPa. For each new pressure amplitude, a fresh concentration of contrast agents is added to the sample chamber, and each composition is repeated in triplicate in order to ensure at least one hundred microbubbles are analyzed for statistical significance. One hundred microbubbles are assured to be analyzed based on the assumption that the concentration of microbubbles within the sample chamber is

0.2 microbubbles per mm3, and is well mixed. Again, a MATLAB script will interpret

the data, and will plot the number of destroyed microbubbles over the total number of

detected microbubbles with increasing peak negative pressure.

199

Figure 6.17: Inertial cavitation threshold of co-encapsulated and un-encapsulated microbubbles.

Results shown are for microbubbles (co-encapsulated [x] and un-encapsulated [o]) with a

bubble shell consisting of 95% DPSC and 5% DSPE-PEG 5000. In both cases, no

cavitation is detected until approximately 0.5 MPa peak negative pressure. In the un-

encapsulated sample, the curve is the typical sigmoidal shape, which is fully cavitated by

1.4 MPa. However, the co-encapsulated sample, in which the microbubbles are shielded by

the outer PLA shell, exhibit less cavitation at the sample peak negative pressures as the un-

encapsulated sample, and never reach complete cavitation within the maximum pressure

which can be generated by the pulser.

The inertial cavitation threshold of the co-encapsulated microbubbles is measured to determine the peak negative pressure they can withstand without being destroyed.

Microbubble samples consisting of 95 mole% DSPC and 5 mole% DSPE-PEG 5000, both co-encapsulated in PLA and un-encapsulated, are tested for their cavitation threshold and shown in Figure 6.17. While both samples exhibit no cavitation until a 200

peak negative pressure of 0.5 MPa, the co-encapsulated sample shields its microbubbles

from cavitation at higher pressures. The pressure at which 50% of the sample is cavitated

for the co-encapsulated microbubbles (1.5 MPa) is almost double that of the un-

encapsulated microbubbles (0.8 MPa), and the pressure at which 100% of the sample is

cavitated for the co-encapsulated sample cannot be determined because it exceeds the

maximum PNP output of the pulser. This result proves that the co-encapsulated contrast agent is safer and longer lasting in an ultrasound field (at PNP values above 0.5 MPa)

than typical microbubbles, through shifting the inertial cavitation threshold to higher

values of pressure. In this way, a clinician is able to image at higher MIs without fear of

the onset of inertial cavitation, therefore generating brighter images while also protecting

the integrity of the patient’s endothelial cells.

6.6.2 Modeling Co-encapsulated Oscillation Behavior

As in Chapter 4, the behavior of microbubbles oscillating within the aqueous core of

polymer microcapsules can be described by some modification of the colloidal model

(Equation 4.10). To describe the limit of the oscillations of a bubble as the bubble radius,

R, approaches the microcapsule radius, Rcap, a drag term can be added to the colloidal

model energy balance, highlighted in bold below in Equation 6.2 (and collected with

Poritsky viscous damping term).

201

3 1 2 3 2 2 ( 2 2) 4 + = + 3훾 1 1 2 2 퐴 표 2 0 ̇ ̇ 퐾 푅 − 푅 푠 ̇ 0 휎 푅 훾푅 휎 푅 휅 푅 푅푅̈ 푅̇ ��푃 � � � � − � − � − � − 표 − 2 휌 푅0 푅 푐 푅 푐 푅푅 푅

+ ( ) ퟑ푹 ퟒ − 흁푹̇ � ퟐ � − 푃0 − 푃 푡 � ퟐ�푹풄풂풑 − 푹� 푹 (Equation 6.2)

The addition of the drag term drastically increases the damping of the oscillation as R

approaches Rcap (the difference is raised to the -2 power). The predicted oscillations as

given in Figure 6.18, for Rcap = ∞, 3, and 4 µm (black, red, and green line, respectively).

From the colloidal model simulations in Chapter 4, the equation is solved with parameters: ρ is 998 kg/m3, P0 is 10.13 kPa, σ is 0.051 N/m, γ is 1.07, µ is 0.001 Pa s, R0

is 1 µm, KA is 50 mN/m, κs is 7 * 10-9 N s/m, and P(t) is the 4 cycle sine wave pressure function with an amplitude of 1 MPa. The case where Rcap = ∞ is equivalent to response

from the colloidal model, Equation 4.10.

Figure 6.18 shows that the oscillations predicted for the co-encapsulated microbubbles

vary from freely oscillating microbubbles (black line) only when R nears Rcap (as R

approaches 92.5% of Rcap). At this point, the repulsion force becomes exponentially

stronger (power -2 from the equation), which makes sense physically as the fluid inside the microcapsule is being compressed by the bubble expansion and more resistant to further compression. Otherwise, the oscillations remain mostly the same for all cases of

Rcap (the lower Rcap responds slightly faster during the negative change in radius because the radius has already stopped expanding by the time it experiences negative pressure). 202

Figure 6.18: Oscillations predicted for co-encapsulated microbubbles. The simulated oscillations

predicted from Equation 6.2 for two values of Rcap, and one from the colloidal model (black

line, infinite Rcap) are displayed. The drag force constraint only affects the microbubble

oscillations as it approaches R = Rcap (Rcap = 4 µm: red line, 3 µm: green line).

6.7 Cavitation Induced Cell Death

It is anticipated that the co-encapsulation of microbubbles within the aqueous core of polymer microcapsules will lend some increase in patient safety during contrast imaging.

This is obviously a hot-button issue for ultrasound contrast agents due to the FDA restrictions mentioned previously. One way of determining the relative safety of a contrast agent under ultrasound is in vitro cell viability. While it is somewhat nebulous 203

as to the mechanism of interaction between living cells and microbubble contrast agents, it is a consensus that microbubble oscillations are the driving force [40, 84, 109-111].

The polymer shell both limits the microbubble oscillations and provides a barrier between

the microbubble and the outer fluid, both of which should prove advantageous in

protecting nearby cells from the negative bioeffects associated with cavitation.

Cell viability can be analyzed by a propidium iodide (PI) cell death assay. In this assay,

PI fluoresces at 550 nm (red) if excited at 488 nm in the presence of DNA. PI’s only

route into through the cell membrane to interact with DNA is assumed to be that of a

sonoporated or dead cell. First, human colon cancer cells (SW-480) cells are cultured to

70% confluence in T75 flasks. SW-480 cells are preferred because of their fast growth

rate and their strong adherence to the walls of the growth chamber. SW-480 cells can be

grown in a modified Dulbecco’s Modification of Eagle’s Medium (DMEM) with sodium

pyruvate, non-essential amino acids and 10% fetal bovine serum (FBS). The day before

the experiment, the cells are trypsinated and moved to Opticells (Thermo Scientific,

Rochester, NY), which are nearly acoustically transparent (cellulose chamber walls). 9.6 ml of cell suspension in DMEM growth media is added to each Opticell (maximum

volume 10 ml). Directly before performing the experiment, 0.1 ml of 1 mg/ml PI in

water is added to the Opticell, along with a total volume of 0.3 ml of the desired contrast

agent concentration. It is important to eliminate as many macroscopic air bubbles from

the Opticell as possible to avoid acoustic reflections.

204

For a single experiment, the Opticell is placed in the focus of a spherically focused 2.25 center frequency transducer (7.5 cm focus). The transducer broadcasts 250 ten cycle pulses at a pulse repetition frequency of 5 Hz. Twenty fluorescence micrographs are recorded in the focal zone of the Opticell before and after sonication. The difference between the mean brightness of the images before sonication and after sonication is then compared (on a brightness intensity scale of 0 - 255). Sample micrographs from before and after sonication of a positive cell death results from 99 mole% DSPC, 1 mole%

DSPE-PEG 3000 (30 million contrast agents/ml concentration, 3 MPa PNP are displayed in Figure 6.19).

205

Figure 6.19: PI fluorescence cell death assay. Micrographs from before (left column) and after (right

column) cell sonication in the presence of contrast agents are displayed for microbubbles

consisting of 5 mole% DSPC, 95 mole% DSPE-PEG 3000 (top row) and the co-

encapsulated contrast agent (bottom row). The un-encapsulated microbubbles under

ultrasound cause significant cell death, as shown by the difference between panels A and B,

where difference in the co-encapsulated before and after is minimal if existent (between C

and D).

The pronounced PI fluorescence in panel B compared to panel A indicates that the

experiment has successfully killed a significant population of the SW-480 cells in the

experiments with un-encapsulated microbubbles, where as the insignificant difference

between panels C and D indicate little cell death in experiments run with the co- encapsulated contrast agent. These results prove that at similar acoustic brightness (and in fact higher concentration per unit contrast agent), the co-encapsulated contrast agent effectively shields surrounding cells from the negative bioeffects – here, cell death – more effectively than un-encapsulated microbubbles. The un-encapsulated microbubbles used in this study are analogous to Definity or SonoVue commercial contrast agents, but can be produced cheaply and quickly.

The results from such micrographs can be quantified by analyzing their brightness using a MATLAB script (imread function). Thresholding is applied to the micrograph (as in

Chapter 2) in order to remove the background and extraneous piece of the image which are not related to PI fluorescence. Figure 6.20 shows the quantified results of experiments which investigate the cell death as a function of the CTR displayed by the given contrast agent composition. By using the results from Section 6.5, the respective 206 contrast agent concentration of the microbubbles and microcapsules can be determined; however, for the purpose of this study it is more interesting to compare the contrast agents by normalizing their acoustic brightness (recall that 125 microparticles give the same brightness as 1 microbubble).

1

0.8

0.6 Bubbles 0.4 Capsules Relative Cell Death Relative 0.2

0 -6 0 2 6 CTR (dB)

Figure 6.20: Cell death as a function of microbubble/capsule concentration. This chart shows the

relative amount of cell death experienced by SW-480 cell lines in the presence of

ultrasound and contrast agents. In the presence of un-encapsulated microbubbles (red bars),

cell death is proportional to CTR (therefore concentration). However, in the presence of the

co-encapsulated formula (blue bars), cell death is insignificantly small and insensitive in

changes in concentration.

207

In Figure 6.20, the safety of the co-encapsulated contrast agent is proven. The cells are

subjected to 3 MPa peak negative pressure in the presence of both un-encapsulated and

co-encapsulated contrast agent. The concentrations of these contrast agents are related in

an earlier experiment and therefore it is represented in the figure as CTR values for the

respective concentrations of the two contrast agents. In other words, the concentrations

of each contrast agent which give a certain CTR value are plotted together in the figure

above. Predictably for microbubble contrast agents, cell death decreases with decreasing

CTR value (and concentration). In the case of the co-encapsulated contrast agent

however, no significant cell death is observed even at the highest concentration (and cell

death remains insignificant as CTR increases).

In addition to cell death as a function of pressure, the same assay can be performed at various ultrasound pressures. In this study, Opticells loaded with a constant concentration of 30 million microbubbles/ml are exposed to pressures of 50, 500, 1000, and 2000 kPa PNP (one Opticell per pressure). The results of this experiment show some

small degree of cell death at the lowest pressures (50 and 500 kPa), and a far greater

degree of cell death at the highest pressures (1 and 2 MPa). This result can be combined

with the previous cavitation profile for the same microbubble composition, shown below

in Figure 6.21.

208

1

0.8

Destroyed 0.6 Relative Cell Death Fraction 0.4 Percent Destroyed Cell Death

0.2

0 0 0.5 1 1.5 2 PNP (MPa)

Figure 6.21: Cell death and cavitation profiles. The relative cell death profile is overlaid with the

cavitation profile for microbubbles with a shell composition of 99 mole% DSPC, 1 mole%

DSPE-PEG 3000. Both graphs exhibit the same trend of a sigmoidal increase beginning at

approximately 0.5 MPa.

Overlaying these results provides a significant insight into the mechanism of cell death in

this study. A small degree of cell death is found at pressures below 0.5 MPa, a region

which is associated with only stable cavitation as determined by the cavitation threshold

for this shell composition. At PNP above 1 MPa, the degree of cell death increases

significantly. These higher pressures are indentified as the inertial cavitation region for this shell composition. This outcome suggests the major mechanism of cell death 209 imposed by oscillating microbubbles is mostly due to inertial cavitation (and to a lesser degree, stable cavitation).

These results suggest that the co-encapsulated contrast agent is successfully providing a barrier between the inertial cavitation of the microbubbles within and the cell population outside the microcapsule. The result is again bounded by the pressure range of the pulser/power amplifier, SchaumSchläger, but it is possible that at high enough peak negative pressure or with some alteration of the microcapsule composition that significant cell death could occur. It is apparently that there exists some trade-off between the robustness of the contrast agent (CTR longevity, cell viability) and the ability to puncture or damage the microcapsule for potential drug delivery applications.

6.8 Co-encapsulation Microcapsule Leakage Studies

The co-encapsulated formula has an obvious application in the drug delivery field based on its relatively large volume of aqueous media encapsulated within the microcapsule along with the microbubbles. For the contrast applications described above, the aqueous media was simply PBS, however this could easily be replaced with a hydrophilic drug solution. The advantage of the co-encapsulated formula over microparticles with no encapsulated microbubbles is the use of inertial cavitation as a potential trigger for drug release. Coupling this with the positioning of the transducer, the co-encapsulated combination could be used as a controlled and targeted drug delivery vehicle. 210

6.8.1 Calcein: self-quenching fluorophore

To more easily analyze drug leakage from the microcapsules, the hydrophilic drug can be

replaced by a hydrophilic fluorescent dye. Calcein, a self-quenching fluorophore, is

selected as the best dye for the study. First, calcein has a relatively small molecular

weight (622 g/mol) which allows for quicker diffusion or active leakage through the

polymer shell. Additionally, as a self-quenching fluorophore, at high concentrations the

calcein molecular interactions quench the fluorescence. This is useful for leakage

experiments because the calcein concentration inside microparticles can be set well above

the concentration for self-quenching, therefore not fluorescing until the dye leaks from

the microcapsule into the larger volume of aqueous outside of the shell.

To properly evaluate the leakage of calcein from the microcapsules, it is important to

select an encapsulated concentration which provides clear fluorescence results as it leaks

from the polymer shell. Quantifying fluorescence intensity of an aqueous sample can be

achieved by fluorescence spectrometry. 3 ml samples of varying concentrations of calcein in water will be analyzed by a fluorescence spectrometer (PTI, Birmingham NJ).

As per the fluorescent properties of calcein, the samples are excited at 475 nm, and the scan reads for emissions between 490-540 nm. Figure 6.22 shows the results of the

calcein concentration calibration, below.

211

3000000

2500000

2000000

1500000

1000000 Fluorescence Intensity

500000

0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 [Calcein] (mM)

Figure 6.22: Calcein concentration calibration. Calcein solutions of 0 - 70 µM are analyzed for their

fluorescence intensity (arbitrary units) using fluorescence spectrometry. The data shows a

fluorescence maximum at 35 µM calcein, which is indicative of the self quenching effects

of the fluorophore at that concentration and above. The data is described with a 4th order

polynomial fit.

The results of the calibration show that calcein under the experimental conditions begins

to self quench at a concentration of 35 µM. At higher concentrations, the fluorescence intensity begins to decline until it ultimately reaches zero (at a concentration of 100 mM).

Therefore, the experiment should be designed such that the concentration of calcein outside of the particles will be on the left side of the self-quenching point so as not to acquire data with an ambiguous result. It is also favorable to have the concentration of 212

calcein encapsulated within the microcapsules to be well above this inflection point.

Accounting for these two factors, the calcein concentration within the particles is selected

to be 70 mM. To calculate calcein concentration from experimental fluorescence

spectrometry results, an empirical 4th order polynomial equation can be employed (from

Figure 6.22). For future reference under these experimental conditions, this relationship is listed below (where IF is the fluorescence intensity in arbitrary units, and Ccal is the

calcein concentration in mM):

11 4 10 3 9 2 8 4 IF = -1.505*10 (Ccal ) + 4.692*10 (Ccal ) - 4.994*10 (Ccal ) + 1.980*10 (Ccal) - 1.0962*10

(Equation 6.3)

While working with calcein for these studies, it was determined that the fluorophore can

give a false positive result (an increase in fluorescence intensity) in the presence of

certain materials. Examples of these materials include nitrile (as in examination gloves),

rubber (as in the housing of the immersion cables for the transducers), and most

significantly latex (as in the material of the sample chamber). In light of this interaction,

it is best to remove all such materials from the experimental procedure. To leak dye from

the microcapsules, it is imperative that they are sonicated in either glass or plastic (both

of which have shown to have no interaction with calcein), and that the cable housing of

the transducer not be submerged in the sample chamber at any point during the course of

the experiment. This strange and unexpected result is studied briefly below in Figure

6.23 for the interactions of calcein specifically with the latex sample chamber several

conditions.

213

400000

350000

300000

250000

200000

150000 Fluorescence Intensity 100000

50000

0 0 10 20 30 40 50 60 70 80 90 Time (min)

Water Calcein Old Chamber New Chamber

Figure 6.23: Interactions between calcein and white latex. A calcein solution is added to a latex

finger cot and mixed for a period of 45 minutes, with fluorescence measurements taken at

regular intervals. The four samples in the figure represent: water mixed in the latex cot (♦),

a calcein solution mixed in the latex cot (■), a calcein solution mixed in a latex cot which

has been soaked in water for 1 week (▲), and the previous calcein solution removed from

its old cot and added to a new one and mixed for an additional 45 minutes (x).

The results of the study provide several insights about the interactions between latex and calcein. First, the sample of water (♦) mixing in the latex cot shows that latex has no inherent fluorescent properties of its own (and neither does water). Also, the calcein solution (■) mixing in the latex cot reaches a maximum of fluorescence intensity after 45 minutes; that is to say that the interactions somehow become saturated after that time.

The mixing of the calcein solution in a latex cot which has soaked in deionized water for 214

1 week (▲) shows that this act has no effect on the interactions between the calcein and latex. Finally if the calcein solution is taken from an old latex cot after 45 minutes of

interaction, and then added to a fresh latex cot (x), the calcein cannot interact further with

the new cot (proven by no increase in fluorescence intensity). In a separate experiment, a

single latex cot is reused with new calcein solution six times. Each time the six calcein

solutions show the exact same growth rate and saturate at the same value of fluorescence

intensity.

Taken together, these results suggest that the latex is somehow affecting the calcein

solution, and not the other way around; because if the calcein were entering the cot, for

example, the intensity would again increase with the addition of a new cot. Additionally,

the ability for the latex to affect the calcein is seemingly limitless, and does not

degenerate with time, water diffusion, or exposure to calcein. While the mechanism of

these interactions is unknown, it is important to bear in mind for ultrasound induced

leakage experiments.

6.8.2 Low Frequency Dye Leakage

The previously prepared double emulsion microcapsules with encapsulated 1:1

microbubble solution (microbubble concentration approximately 1 billion bubbles per

ml) in PBS and 70 mM calcein buffer are actively leaked by ultrasound. The

microcapsules are effectively leaked by sonicating them with a 24 kHz probe sonicator

for a total time of 5 minutes. This is a somewhat trivial result for a few reasons. First,

low frequency ultrasound is dangerous for living tissue, as the long wavelength allows 215 the material to fully respond to the pressure amplitude, as well as nucleating and subsequently cavitating trapped and dissolved gasses. Additionally, co-encapsulated microbubbles will be oscillating at a frequency very far from their resonance frequency

(as discussed earlier in Chapter 4), and their effect on the polymer shell should be less than at their resonance frequency. Finally, during the microcapsule synthesis process, the drying phase needs to be arrested after only 30 minutes in order to achieve any degree of leakage. This is most likely due to the fluidity of the membrane while it still retains some of the organic solution. However, the resulting studies can still provide some proof of concept of ultrasound induced leakage from a microcapsule with some polymer shell architecture.

To view calcein fluorescence under a fluorescent microscope (Axioskop 2, Carl Zeiss,

Heidenheim, Germany), it is excited at 470 +/- 20 nm, and viewed between 525 +/- 25 nm. Dye release from microcapsules is measured by active leakage with ultrasound followed by detection by fluorescence analysis. The results of the low frequency ultrasound (24 kHz, Misonix, Farmingdale, NY) experiment are shown in Figure 6.24 A-

D. Here, microscope images are recorded before (Figure 6.24 A-B) and after (Figure

6.24 C-D) ultrasound with both light (Figure 6.24 A, C) and fluorescence (Figure 6.24 B,

D) microscopy.

216

Figure 6.24: Fluorescent dye leakage with low frequency ultrasound. Microscope light and

fluorescence images of fluorescent dye loaded microcapsules before and after 5 minutes of

continuous wave application of 24 kHz ultrasound are shown. Fluorescent excitation light

was at 470 +/- 20 nm, and optical filter allows viewing at 525 +/- 25 nm. a microcapsules

under visible light before ultrasound, b microcapsules under fluorescent light before

ultrasound, c microcapsules under visible light after ultrasound, d microcapsules under

fluorescent light after ultrasound.

In the images before ultrasound, it is evident that most of the fluorescent dye is contained within the particles when the fluorescent image is recorded and compared to the phase inversion. After 5 minutes of 24 kHz ultrasound, the images are retaken and it becomes evident that some of the dye has leaked out of the particle and into the surrounding fluid by the dramatic increase in the amount of fluorescence present in the media surrounding the microcapsules. These fluorescence results can be quantified with the fluorescence spectrometer used to measure the calcein concentrations, and the results of the same study are displayed in Figure 6.25.

217

120000

100000

80000

60000

40000 Leakage (arbitrary units) (arbitrary Leakage

20000

0 0 1 2 3 4 5 6 Sonication time (min)

Sample (With Ultrasound) Control (No Ultrasound)

Figure 6.25: Active ultrasound leakage from co-encapsulated microcapsules. A solution of co-

encapsulated microcapsules with 1:1 70 mM calcein buffer to microbubble solution is

sonicated at 24 kHz for a total of 5 minutes. At 1 minute intervals, the sample is tested for

its fluorescence intensity on a fluorescence spectrometer. The results are also subtracted

from a control sample of co-encapsulated microcapsules which do not undergo any

sonication (the zero line). The results show that microcapsule exhibit some quick burst

release in the first minute of sonication, and then plateau with increasing sonication time.

In Figure 6.25, a burst release of calcein is observed from the microcapsules followed by a plateau in dye leakage. The effect of passive diffusion has been subtracted from the dye release profile, and is a minimal contribution compared to the active leakage caused by ultrasound. Although this result is encouraging, it is still not clinically relevant because of the use of the low frequency (24 MHz) probe transducer. For the result to be 218

interesting for in vivo studies in drug delivery, the microcapsules need to actively leak

the drug with a high frequency ultrasound transducer, like those found in a clinical

environment.

6.8.3 Clinical Frequency Dye Leakage

Unfortunately, high frequency ultrasound therapy at 2.25 MHz and 3 MPa PNP is insufficient to cause significant dye leakage from the PLA microcapsules synthesized in this chapter. This is most likely due to the rigid solid polymer shell which encapsulates the microbubbles. It is yet unclear whether the polymer shell is somehow inhibiting the microbubbles from undergoing inertial cavitation (either by signal or oscillation shielding) or that microbubble inertial cavitation is not powerful enough to cause sufficient damage to the polymer shell for it to release any dye. As it is well known that cells (with their mainly lipid/protein bilayer) can be sonoporated by inertially cavitating microbubbles [40], the outer shell should optimally be a lipid vesicle.

However, encapsulating pre-prepared microbubbles within the aqueous core of a lipid

vesicle is not a simple task. Attempts to arrive a co-encapsulated vesicle through vesicle electroformation and microinjection were unsuccessful. Spontaneous formation through either electroformation or rehydration have been unsuccessful due to the mechanism in which lipid films form into giant uni-lamellar vesicles (GUVs), the process of which

shown in Figure 6.26, which is adopted from Sriram [112].

219

Figure 6.26: Mechanism of vesicle budding from a bilayer. This mechanism, proposed here by

Sriram [112], shows the bilayer progression as the vesicle buds from the membrane. In this

way, it would be difficult for microbubbles to enter into the membrane as there are no large

gaps in the bilayer during the budding process.

The mechanism of vesicle creation proposed here is budding. Since the bilayer buds off to form the vesicle, there are no windows in which a large 1 µm microbubble will be able to slip past the membrane into the vesicle. This mechanism does provide insight on which encapsulation techniques will be successful at trapping microbubbles. For example, a mechanism in which a bilayer is stretched across interface between an aqueous solution, and a solution with microbubbles would allow for the budding of vesicle into the aqueous solution from the microbubble solution, therefore having an inner phase with encapsulated microbubbles. An analogous set up developed by

Funakoshi [113] for synthesizing GUVs with encapsulated drug, is displayed in Figure

6.27, below.

220

Figure 6.27: Pulse jet vesicle synthesis. This diagram, adopted from Funakoshi [113], details a method

of producing GUVs by pulse jet formation. This technique involves pulsing a jet of the

soon to be encapsulated solution through a planar lipid membrane in order to bud off a

vesicle into the aqueous buffer on the other side of the bilayer.

In Figure 6.27, Funakosi diagrams the design of a GUV synthesis technique involving jetting the encapsulated media from a nozzle at a lipid bilayer, thus forcing a vesicle to bud. In Funakoshi’s case, the encapsulated material was a drug; however in the case of co-encapsulation, the encapsulated solution would ideally contain microbubbles and a drug. This technique, along with the possibility of forming liposomes with a double emulsion, is a potential method of encapsulating microbubbles within the aqueous core of a liposome, although these experiments have not been pursued in this study.

6.9 Conclusion

221

Given these results, the novel co-encapsulation of phospholipid microbubbles within

polymer microcapsules shows that when exposed to an ultrasound field yields the

expected acoustic response, along with providing successful contrast to ultrasound

images. As expected, the co-encapsulated contrast agent provides the added benefit of

shielding the microbubbles within from the ultrasound wave, which is shown to

effectively double their inertial cavitation threshold. Additionally, the co-encapsulated

contrast agent has shown to have an acoustic response similar to the commercial contrast

agent, SonoVue and Definity, and in the case of higher ultrasound MIs, as seen in Figure

6.14 A, C, the co-encapsulated contrast agent has a slightly longer lifetime than that of

SonoVue.

In addition to the potential benefits offered in contrast, the co-encapsulated formula also

has potential benefits as a drug delivery vehicle. The size of the PLA microcapsules (3-5

µm), is ideal for balancing maximum loading potential of a water soluble drug while still

maintaining a suitable size for vascular and capillary transport. While Figure 6.24 shows

that a hydrophilic dye can be successfully leaked from the co-encapsulated sample with

low frequency ultrasound, it is understood that this is not a physiologically relevant result

since low frequency ultrasound has shown to cause damage to tissue [20]; however,

studies are underway to investigate the feasibility of leakage at higher, clinically relevant

frequencies (1-10 MHz). Thus far, the microbubble cavitation that is able to be generated with high frequency ultrasound, as in Figure 6.17, is unable to release any dye from the current microcapsule formula.

222

In this chapter, the acoustic response generated by the co-encapsulation of phospholipid shelled microbubbles within the aqueous core of polymer microcapsules is examined along with its feasibility as an ultrasound contrast agent. The addition of the polymer shell provides the added benefit of approximately doubling the inertial cavitation threshold of the microbubbles contained within. The feasibility of the utilization of the co-encapsulated contrast agent as a drug delivery vehicle was also investigated. It is concluded that the co-encapsulated contrast agent provides contrast similar to that of un- encapsulated microbubbles, both in acoustic response and image intensity of contrast to tissue.

223

CHAPTER 7: Summary and Implications

Over the course of this dissertation, the colloidal science of contrast agents have been

examined and hopefully better understood. The following sections summarize the

findings of each chapter in this dissertation and describe the potential implications and

future of the study.

7.1 Project Summary

The size distributions of populations of microbubbles were examined with a variety of different shell compositions. This set of shell compositions was laid out, which contained combinations of DPSC and DSPE-PEG, mole fractions between 0.01 – 0.15

DSPE-PEG, and PEG molecular weights between 1000 and 5000 g/mole. It was found that the size distributions are very similar for all the shell compositions measured; they contained a monomodal peak with a nearly Gaussian distribution. The mean size of the microbubbles did not change significantly for the compositional changes made in this study. Additionally, an image segmentation rationale was presented for measuring the size distribution of microbubbles.

This same set of shell compositions is then analyzed for their inertial cavitation threshold pressure. A high voltage pulser, the SchaumSchläger, was specifically designed, 224

synthesized, and utilized in these experiments. A MATLAB program analyzes the

acoustic response of the microbubbles to determine their destruction through double

passive cavitation detection. The experiments yielded the result that the inertial

cavitation threshold of these microbubbles is between 0.75 and 1.25 MPa. More

interestingly, as PEG mole fraction increases, the inertial cavitation threshold increases

sigmoidally. With increasing PEG molecular weight, however, the cavitation threshold is

shown to decrease slightly. These results can be fit with a RPNNP like equation

(Morgan’s equation) by numerically solving it for a cavitation criterion – here when R =

2R0. It is also shown that limiting the size distribution has the effect of sharpening the

increase of the cavitation profile.

With these experimental cavitation results, a predictive model is desired to explain the data. Previously developed models for microbubble oscillations are examined and compared. Based on the colloidal science principles, a new model for the oscillation of thinly shelled microbubbles is explained. For simple microbubble compositions, a predictive model can be applied for calculating material parameters of the microbubble shell. This equation is shown to hold for the experimental cavitation data collected during the course of this work.

This same set of microbubble shell compositions described earlier is then analyzed for their resonance frequency. This is accomplished by measuring the attenuation of a broadband chirp signal sent through a field of microbubbles. The frequency where the attenuation is the most is that at which the microbubbles have absorbed the most energy, 225

i.e. the resonance frequency. Again, several trends exist as a function of the shell

composition. As PEG mol fraction and molecular weight increase, the resonance

frequency decreases (again sigmoidally). The experimentally measured resonance

frequencies can be fit with a simple model by Lars Hoff to describe sound moving

through a field of bubbles.

Using the information gathered in the previous chapters, a novel contrast agent was

designed. The contrast agent is comprised of lipid shelled microbubbles floating within

the aqueous core of polymer shell microcapsules. This combination has the benefit of

added patient safety (through the aversion of cell death) while providing similar contrast

to commercially available contrast agents. The contrast agent accomplishes this by

shielding the microbubbles from the incident sound pressure and preventing their

expansion beyond the threshold radius. The design of the contrast agent is also

inherently a drug delivery vehicle which can cater to both hydrophilic and hydrophobic

drugs.

7.2 Implications

The implications of this work can mainly be broken down into the two main sections of

study, the physical properties of microbubbles as a function of shell chemistry and the

design of a novel contrast agent.

226

Understanding the inertial cavitation threshold of a microbubble allows a clinician to dial

in a certain acoustic pressure (through the MI) to avoid cavitation in imaging scenarios.

On the other hand, in future drug delivery applications, the pressure could be raised above the cavitation threshold to encourage leakage. This simple method presented can be used to determine these thresholds for any number of contrast agents, as only a few simple mixtures have been presented here. Additionally, microbubble contrast agents could be designed with a specific application in mind, such as to tailor the cavitation threshold to the needs of a specific scan type or transducer frequency. Knowing the resonance frequency of microbubbles also effects their image quality; the closer to the resonance frequency, the brighter the contrast and the greater the oscillations. The potentially violent and damaging effects of inertial cavitation coupled with the legal struggles of contrast agents to gain mainstream acceptance make this technique of importance.

With this in mind, the new contrast agent seeks to limit the microbubble’s ability to inertially cavitate, while still providing contrast brightness. This has great implications in the aforementioned legal battle (assuming that inertial cavitation is the mechanism of the negative implications). Also, the use of this contrast agent as a drug delivery vehicle would make it perfectly suitable as a controlled and target delivery mechanism. The interactions of ultrasound and the microbubbles control when and if the drug will release from the microcapsule, and the physical location of the ultrasound transducer defines the targeted regime (focused transducers can make the target even more exact). However, this work is not yet complete. 227

7.3 Future Outlook

There are many potential avenues to pursue in the advancement of these studies. First, in

the study of the microbubble physics, there is a need for more raw data to interpret. The

set of shell compositions studied truly only delve into the effect of the addition of the

stabilizing PEG to the monolayer. It is complete in the sense that a full range of PEG

mole percentages have been study, since above 15 mole% PEG no more PEGylated lipids

will be able to associate into the membrane. The effect of PEG molecular weight would

also be difficult to explore further, but perhaps PEG molecular weights as low as 100

g/mole can be tested in conjunction with the predictive model.

To fully discover shell effects, these types of experiments would need to be performed on

different lipids, such as dipalmitoyl phospatidylcholine (DLPC, a 16 chain saturated

lipid) and diarachidoyl phospatidylcholine (DAPC, a 20 chain saturated lipid). If the

temperature were lowered below 25 oC, than lower carbon chain length lipids and unsaturated lipids could be tested as well (their melting temperatures are below room temperature). Hydrophilic polymers other than PEG can be used as the stabilizer.

Commercial microbubble contrast agents, like Definity, have several other degrees of complexity besides these. In fact Definity has a lipid blend with a blend of PEGylated lipids. Additionally it is further stabilized by a viscous liquid (more than water and PBS).

All of these variables will have some effect on the microbubble’s oscillation behavior, 228

and therefore their cavitation profile. In terms of the developed colloidal microbubble

dynamic equation, it may be possible to linearize this equation in a similar approach as

Neppiras and Morgan [30, 54], which would allow for determination of the microbubble

resonance frequency as a function of the predictive KA parameter. These newly

determined resonance frequencies could be compared to experiment and perhaps provide

a predictive model for both inertial cavitation and resonance frequency.

A great deal of work can be done in furthering the development of the co-encapsulated

contrast agent. For the formula described above, there are many possibilities for

improving the contrast brightness (CTR) of the microparticles. First, the microbubble to

microcapsule ratio should be investigated to find the optimal amount which produces the

most brightness. This is most likely a tradeoff between the brightness caused by the

increase in microbubbles and the multiple scattering effects which would be present if too

many bubbles were oscillating in near proximity (like inside the microcapsule).

The co-encapsulation formula was initially developed as a drug delivery platform.

Unfortunately the current formulation has proven to be very difficult leak using the

microbubbles as a trigger, whether it is because the microbubbles do not oscillate enough

or that the shell is too tough to rupture. However, as mentioned in Section 6.7.2, the

feasibility of leaking a drug from a liposomal carrier is much higher than from a polymer

shell. A lipid bilayer encapsulation shell would most probably allow for drug delivery

applications at acoustic pressures (or MIs) above the inertial cavitation threshold, while

providing superior contrast (over the polymer particles) at pressures below the inertial 229 cavitation threshold, thus giving it multiple functions. The brightness would likely be great in a liposome because the walls of a liposome are more flexible they will reflect less sound. As a glimpse of the future for this work, Figure 7.1 displays a microparticle which has ruptured by some artifact of SEM preparation (most likely lyophilization).

However accidentally, this image represents the true potential of this research.

Figure 7.1: Ruptured co-encapsulation microcapsule. While the rupture of this microparticle is an

artifact of SEM preparation, it shows the potential for leaking drugs from its aqueous core. 230

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APPENDIX A: List of Abbreviations

A-mode Amplitude mode

B-mode Brightness mode

CTR Contrast to tissue ratio [dB]

DAPC Diarachidoyl phosphatidylcholine

DLS Dynamic light scattering

DMEM Dulbecco’s Modification of Eagle’s Medium

DPPC Dipalmitoyl phosphatidylcholine

DSPC Distearoyl phosphatidylcholine

DSPE Distearoyl phosphotidylethanolamine

FBS Fetal bovine serum

GUV Giant uni-lamellar vesicle

MI Mechanical index

MW Molecular weight [g/mole]

PBS Phosphate buffered saline

PEG Polyethylene glycol

PI Propidium iodide

PLA Polylactic acid

PNP Peak negative pressure [Pa]

PT0 inertial cavitation threshold pressure [Pa] 242

PT50 Pressure required to inertially cavitate 50% of microbubbles in a population [Pa]

PT100 Pressure required to inertially cavitate 100% of microbubbles in a population [Pa]

PVA Polyvinyl alcohol

RPNNP Rayleigh-Plesset-Neppiras-Noltingk-Poritsky (equation)

SEM Scanning electron microscope

SF6 Sulfur hexafluoride

THI Tissue harmonic imaging

W/O/W Water in oil in water

243

APPENDIX B: List of Symbols

α total attenuation [dB]

αt non-dimensional area difference

χ shell elastic modulus [N/m]

∆ adsorption energy [J]

δ damping constant

ε shell thickness [m]

γ polytropic gas constant

κs dilatational viscosity [N s/m]

λ wavelength [m]

µL media viscosity [Pa s]

µsh shell viscosity [Pa s]

3 ρL media density [kg/m ]

σ interfacial tension [N/m]

2 σe extinction cross section [m ]

τ tension [N/m]

Ω dimensionless angular frequency

ω angular driving frequency [Hz]

ω0 naked bubble angular resonance frequency [Hz]

ωr angular resonance frequency [Hz] 244

A area [m2]

2 A0 initial area [m ]

ae microbubble size distribution [m] c media speed of sound [m/s]

Ccal calcein concentration [mM] dse shell thickness [m]

e error

f frequency [Hz]

Fe experimental fraction destroyed at a given pressure

Ft theoretical fraction destroyed at a given pressure

GS shear modulus [Pa]

IF fluorescence intensity [arb] k stiffness [kg/s2]

KA area expansion modulus [N/m] m mass [kg]

MWP polymer functionalized lipid molecular weight [g/mole]

MWL lipid molecular weight [g/mole]

N number of PEG repeat units

NA Avogadro’s number [molecules/mole]

NL lipids per microbubble [molecules]

P mole fraction of polymer in shell

P0 hydrostatic pressure [Pa]

P(t) incident pressure function [Pa] 245

R bubble radius [m]

bubble wall velocity [m/s]

퐑̇ bubble wall acceleration [m/s2] ̈ R퐑0 microbubble resting radius [m]

Rcap microcapsule radius [m]

Sp shell stiffness parameter [N/m]

ttravel travel time [s]

Vs pulser set voltage [V]

X0 PEG mole fraction

Z acoustic impedance [Rayl]

z object distance [m]

246

VITA

Stephen Dicker was born September 6, 1983 (coincidentally one day after Labor Day), in Philadelphia, PA. He graduated the illustrious Abington Senior High School in 2002, and received his bachelor of science in chemical engineering from The Pennsylvania State University in 2006. After graduating from Penn State, he worked for a single year in the vaccines division of Merck & Co., Inc, in West Point, PA. This work proved somewhat unsatisfactory, and in 2007 Stephen decided to pursue a doctorate of philosophy at Drexel University.

At Drexel, Stephen was mentored by Dr. Steven Parker Wrenn, a colloids and surface chemistry expert, in the biological colloids laboratory. Stephen went on to specialize in the synthesis and physical characterization of lipid shelled microbubbles, and co-authored a patent of a novel contrast agent with his advisor. His published works during the course of his Ph.D. include:

1.Stephen Dicker, Michał Mleczko, Georg Schmitz, Steven P. Wrenn. ‘Size Distribution of Microbubbles as a Function of Shell Composition’. (in preparation) 2. Stephen Dicker, Michał Mleczko, Monica Siepmann, Georg Schmitz, and Steven P. Wrenn. ‘Resonance frequency determination of lipid shelled microbubbles’. (in review) 3. Stephen Dicker, Michał Mleczko, Karin Hensel, Georg Schmitz, Alexandra Bartolomeo, and Steven P. Wrenn. 'Coencapsulation of lipid microbubbles within polymer microcapsules for contrast applications'. Bubble Science Technology & Engineering, 2011, 3, 12-19 4. Stephen Dicker, Michał Mleczko, Georg Schmitz, and Steven P. Wrenn: 'Determination of microbubble cavitation threshold pressure as function of shell chemistry', Bubble Science, Engineering & Technology, 2010, 2, 55-64 5. Steven P. Wrenn, Stephen M. Dicker, Eleanor F. Small, Nily R. Dan, Michał Mleczko, Georg Schmitz, and Peter A. Lewin. ‘Busting Bubbles and Bilayers’. Theragnistics, 2012. 6. Steven P. Wrenn, Stephen Dicker, Abdelouahid Maghnouj, Stephan A. Hahn, Michal Mleczko, Karin Hensel, and Georg Schmitz. 'Microcapsules: Reverse Sonoporation and Long-lasting, Safe Contrast'. Proc. 31st International Acoustical Imaging Symposium, Warsaw, Poland, 2011. 7. Michał Mleczko, Stephen M. Dicker, Steven P. Wrenn, and Georg Schmitz. 'Influence of Microbubble Shell Chemistry on the Destruction Threshold of Ultrasound Contrast Agent Microbubbles'. Proc. 31st International Acoustical Imaging Symposium, Warsaw, Poland, 2011. 8. Michał Mleczko, Stephen M. Dicker, Georg Schmitz, and Steven P. Wrenn: 'Determination of the inertial cavitation threshold of ultrasound contrast agents', Proc. BMT, Rostock, Germany, 2010. 9. Steven P. Wrenn, Stephen M. Dicker, Eleanor Small, and Michał Mleczko: 'Controlling Cavitation for Controlled Release', Proc. IEEE Int. Ultrason. Symp., Rome, Italy 2009